How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential

Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is decribed by a matrix of dimension three. It turns out not to be diagonalizable for a critical strength of the interaction, also indicated by the transition of two real into a pair of complex energy eigenvalues. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two.Comment: 5 page

Dynamics in Several Complex Variables

In this chapter we shall describe the dynamics of holomorphic self-maps of taut manifolds, and in particular the dynamics of holomorphic self-maps of convex and strongly pseudoconvex domains. A main tool in this exploration will be provided by the Kobayashi distance

An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Fatou flowers and parabolic curves

In this survey we collect the main results known up to now (July 2015) regarding possible generalizations to several complex variables of the classical Leau-Fatou flower theorem about holomorphic parabolic dynamics

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

Characteristics of maize cultivars in Africa: how modern are they and how many do smallholder farmers grow?

Open Access Journal; Published online: 17 March 2017Maize is the most important cereal and most widely cultivated staple that plays a key role in the food security of sub-Saharan Africa (SSA). Although some countries have achieved significant gains in maize productivity, the SSA average yields are far below what could be obtained with improved cultivars under good crop management. Low cultivar turnover is one among many contributing factors to low maize yields in SSA. At present, there is a critical knowledge gap on the identity, number, and age of maize cultivars currently grown by smallholder farmers on the continent. Results This study revealed that nearly 500 maize cultivars were grown in 13 African countries surveyed in the 2013/2014 main crop season. Sixty-nine percent of the cultivars each occupied 40% and four occupied >30% area. Approximately 32% of all the cultivars were hybrids, 23% were improved open-pollinated varieties (OPVs), and 46% were locals. Eastern Africa (EA) and southern Africa (SA) accounted for about 43 and 38%, respectively, of all the cultivars reported, whereas West Africa’s (WA) share was 19%. The average area planted to modern cultivars in the surveyed areas was estimated at 57%—with EA, SA, and WA estimates of 82, 55, and 36%, respectively; however, increased adoption was not necessarily always related to improved productivity, as the latter depends on many additional factors. Each household planted an average of 1.781 cultivars (range 1–8). The overall weighted average age of the cultivars was 15 years, with hybrids and OPVs being 13 and 18 years, respectively. Conclusions Maize variety turnover in SSA is slower than what is practiced in the USA and other world regions such as Latin America and Asia. The substantial variations among regions and countries in all parameters measured suggest a tailored approach to mitigation interventions. Findings of this current study pave the way for replacing the old cultivars with more recent releases that are tolerant or resistant to multiple stresses and are more resilient

Holomorphic linearization of commuting germs of holomorphic maps

Let $f_1, ..., f_h$ be $h\ge 2$ germs of biholomorphisms of \C^n fixing the origin. We investigate the shape a (formal) simultaneous linearization of the given germs can have, and we prove that if $f_1, ..., f_h$ commute and their linear parts are almost simultaneously Jordanizable then they are simultaneously formally linearizable. We next introduce a simultaneous Brjuno-type condition and prove that, in case the linear terms of the germs are diagonalizable, if the germs commutes and our Brjuno-type condition holds, then they are holomorphically simultaneously linerizable. This answers to a multi-dimensional version of a problem raised by Moser.Comment: 24 pages; final version with erratum (My original paper failed to cite the work of L. Stolovitch [ArXiv:math/0506052v2]); J. Geom. Anal. 201

Valuation of marine plastic pollution in the European Arctic: Applying an integrated choice and latent variable model to contingent valuation

Despite its remoteness, marine plastic pollution is a significant environmental problem in the Arctic. In Svalbard, for example, plastics are found on the shorelines, in the water column, on the ocean floor and in the ice. Organisms have been observed to be entangled in nets and ingestion of plastics has been documented in a range of organisms. Notably almost all Arctic bird species have been found to have ingested plastic, with Northern fulmars being particularly affected, with 89 % of samples recorded as having ingested plastic. Identification and valuation of ecosystem services affected by marine plastic pollution can provide input for decision makers in evaluating and comparing management policies concerning this unique environment. This study employs the contingent valuation method (CVM) for eliciting the willingness to pay (WTP) of Norwegian households for reducing marine plastic pollution around the archipelago of Svalbard. An Integrated Choice and Latent Variable model (ICLV) is employed to explore attitudinal determinants of WTP. We find an average WTP for an initiative to reduce marine plastics of NOK 5,485 (USD 642) per household per year. The ICLV results reveal that people who are relatively more concerned about marine plastic pollution and who deem the proposed initiative effective are willing to pay more (up to 85 % and 50 %, respectively). The use of ICLV models in CVM and recommendations for future research are discussed

Highly efficient planar perovskite solar cells through band alignment engineering

The simplification of perovskite solar cells (PSCs), by replacing the mesoporous electron selective layer (ESL) with a planar one, is advantageous for large-scale manufacturing. PSCs with a planar TiO2 ESL have been demonstrated, but these exhibit unstabilized power conversion efficiencies (PCEs). Herein we show that planar PSCs using TiO2 are inherently limited due to conduction band misalignment and demonstrate, with a variety of characterization techniques, for the first time that SnO2 achieves a barrier-free energetic configuration, obtaining almost hysteresis-free PCEs of over 18% with record high voltages of up to 1.19 V

An application of robust parameter design using an alternative to Taguchi methods

The factors of interest in designing a product or process can generally be classified into two categories, controllable and uncontrollable. Controllable (or control) factors represent those factors which can be regulated. Examples of control factors include: the choice of material, flow rates, processing pressures, times and temperatures. Uncontrollable (noise) factors are those that are either difficult, impossible or too expensive to control during actual production or use. Examples of noise factors are: environmental conditions such as ambient temperature or humidity, process parameters which are dictated by an outside source such as end user demand, and usage factors such as how long and at what temperature a consumer stores a product. As compared to the current Tagachi approach, a new design method which provides greater flexibility in the design of the experiment, utilize a more meaningful performance statistic, and lend itself to a better understanding of the product or process is described in this paper