Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Constraints to the sustainability of a ‘systematised’ approach to livestock marketing amongst smallholder cattle producers in South Africa

Commercialization of smallholder agriculture in South Africa is underpinned by reforms to improve livestock off-take in communal areas and engage smallholder farmers with formal markets. To achieve this, Custom Feeding Programmes (CFPs) were established to improve the condition of communal cattle prior to their sale into formal markets and to ‘systematise’ the informal marketing of cattle in communal areas by enabling participants to achieve higher informal market prices. We evaluate the sustainability of eight CFPs located in Eastern Cape Province in terms of their ability to add value to smallholder cattle production and encourage market participation. Communities with CFPs achieved a 16.6% mean cattle off-take rate, substantially higher than in most communal systems. Furthermore, cattle sold through CFPs attained a 17% higher mean selling price than those sold through other marketing channels. However, these benefits were mainly realized by better-off farmers with larger cattle herds and greater ability to transport animals to and from CFPs. More marginalized farmers, particularly women, had low participation. CFPs also face challenges to their sustainability, including inconsistent feed and water supplies, poor infrastructure and high staff turnover. Key to enhancing participation in CFPs, will be improving the way they are supported and embedded within communities

Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page

Expression of invasion-related extracellular matrix molecules in human glioblastoma versus intracerebral lung adenocarcinoma metastasis

Tumor cell invasion into the surrounding brain tissue is mainly responsible for the failure of radical surgical resection, with tumor recurrence in the form of microdisseminated disease. Extracellular matrix (ECM)-related molecules and their receptors predominantly participate in the invasion process, including cell adhesion to the surrounding microenvironment and cell migration. The extent of infiltration of the healthy brain by malignant tumors strongly depends on the tumor cell type. Malignant gliomas show much more intensive peritumoral invasion than do metastatic tumors. In this study, the mRNA expression of 30 invasion-related molecules (twenty-one ECM components, two related receptors, and seven ECM-related enzymes) was investigated by quantitative reverse transcriptase-polymerase chain reaction. Fresh frozen human tissue samples from glioblastoma (GBM), intracerebral lung adenocarcinoma metastasis, and normal brain were evaluated. Significant differences were established for 24 of the 30 molecules. To confirm our results at the protein level, immunohistochemical analysis of seven molecules was performed (agrin, neurocan, syndecan, versican, matrix metalloproteinase 2 [MMP-2], MMP-9, and hyaluronan). Determining the differences in the levels of invasion-related molecules for tumors of different origins can help to identify the exact molecular mechanisms that facilitate peritumoral infiltration by glioblastoma cells. These results should allow the selection of target molecules for potential chemotherapeutic agents directed against highly invasive malignant gliomas

Unpacking the ‘Emergent Farmer’ Concept in Agrarian Reform:Evidence from Livestock Farmers in South Africa

South Africa has historically perpetuated a dual system of freehold commercial and communal subsistence farming. To bridge these extremes, agrarian reform policies have encouraged the creation of a class of ‘emergent’, commercially oriented farmers. However, these policies consider ‘emergent’ farmers as a homogeneous group of land reform beneficiaries, with limited appreciation of the class differences between them, and do little to support the rise of a ‘middle’ group of producers able to bridge that gap. This article uses a case study of livestock farmers in Eastern Cape Province to critique the ‘emergent farmer’ concept. The authors identify three broad categories of farmers within the emergent livestock sector: a large group who, despite having accessed private farms, remain effectively subsistence farmers; a smaller group of small/medium-scale commercial producers who have communal farming origins and most closely approximate to ‘emergent’ farmers; and an elite group of large-scale, fully commercialized farmers, whose emergence has been facilitated primarily by access to capital and a desire to invest in alternative business ventures. On this basis the authors suggest that current agrarian reform policies need considerable refocusing if they are to effectively facilitate the emergence of a ‘middle’ group of smallholder commercial farmers from communal systems

Comparative study of polar and semipolar (1122) InGaN layers grown by metalorganic vapour phase epitaxy

InGaN layers were grown simultaneously on (11¯22) GaN and (0001) GaN templates by metalorganic vapour phase epitaxy. At higher growth temperature ( 750oC), the indium content (<15%) of the (11¯22) and (0001) InGaN layers was similar. However, for temperatures less than 750oC, the indium content of the (11¯22) InGaN layers (15 - 26%) was generally lower than those with (0001) orientation (15 - 32%). The compositional deviation was attributed to the different strain relaxations between the (11¯22) and (0001) InGaN layers. Room temperature photoluminescence measurements of the (11¯22) InGaN layers showed an emission wavelength that shifts gradually from 380 nm to 580 nm with decreasing growth temperature (or increasing indium composition). The peak emission wavelength of the (11 ¯22) InGaN layers with an indium content of more than 10% blue-shifted a constant value of (50 - 60) nm when using higher excitation power densities. This blue-shift was attributed to band lling effects in the layers.This work was nancially supported by the EU-FP7 ALIGHT project, under agreement no. FP7-280587. This work was also partially supported by the Programme for Research in Third Level Institutions (PRTLI) fourth and fth cycles. SNA acknowledges nancial support for his postgraduate fellowship from the Iranian Ministry of Science, Research and Technology. PJP acknowledges nancial support for his Professorship from Science Foundation Ireland.This is the accepted manuscript. The final version is available from AIP at http://scitation.aip.org/content/aip/journal/jap/116/15/10.1063/1.489856

Twist Deformations of the Supersymmetric Quantum Mechanics

The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.Comment: 18 pages; two references adde

Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry and iii) the -x^4-potential, which serves as a toy model for the quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos correcte

Expression of Distal-less, dachshund, and optomotor blind in Neanthes arenaceodentata (Annelida, Nereididae) does not support homology of appendage-forming mechanisms across the Bilateria

The similarity in the genetic regulation of arthropod and vertebrate appendage formation has been interpreted as the product of a plesiomorphic gene network that was primitively involved in bilaterian appendage development and co-opted to build appendages (in modern phyla) that are not historically related as structures. Data from lophotrochozoans are needed to clarify the pervasiveness of plesiomorphic appendage forming mechanisms. We assayed the expression of three arthropod and vertebrate limb gene orthologs, Distal-less (Dll), dachshund (dac), and optomotor blind (omb), in direct-developing juveniles of the polychaete Neanthes arenaceodentata. Parapodial Dll expression marks premorphogenetic notopodia and neuropodia, becoming restricted to the bases of notopodial cirri and to ventral portions of neuropodia. In outgrowing cephalic appendages, Dll activity is primarily restricted to proximal domains. Dll expression is also prominent in the brain. dac expression occurs in the brain, nerve cord ganglia, a pair of pharyngeal ganglia, presumed interneurons linking a pair of segmental nerves, and in newly differentiating mesoderm. Domains of omb expression include the brain, nerve cord ganglia, one pair of anterior cirri, presumed precursors of dorsal musculature, and the same pharyngeal ganglia and presumed interneurons that express dac. Contrary to their roles in outgrowing arthropod and vertebrate appendages, Dll, dac, and omb lack comparable expression in Neanthes appendages, implying independent evolution of annelid appendage development. We infer that parapodia and arthropodia are not structurally or mechanistically homologous (but their primordia might be), that Dll’s ancestral bilaterian function was in sensory and central nervous system differentiation, and that locomotory appendages possibly evolved from sensory outgrowths