Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.Comment: 14 page

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.Comment: 13 pages, 11 Figure

Fit-for-purpose: developing curriculum for meeting the needs of public health leaders in the 21st century

Although leadership is a well-known concept within organisational science, public health leadership is still not well-defined. Further, leadership is not commonly included in most public health training programs. Faced with immense changes in population health needs, public health professionals require a broader range of skills and expertise than ever before. In response to these issues the article aims to describe the development of a public health leadership curriculum as part of the European project entitled "Leaders for European Public Health" (LEPHIE) supported by the European Commission Lifelong Learning Programme. The article first discusses the theoretical underpinnings related to the public health leadership curriculum development. Secondly, its mission and objectives will be discussed. Thirdly, the methodological approaches and architecture of the programme are presented, and finally illustrates the features for quality assurance and the potential for future use in different contexts

Ab initio Folding Potentials for Nucleon-Nucleus Scattering based on NCSM One-Body Densities

Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series. Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei. We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from $^4$He, $^{6}$He, $^{12}$C, and $^{16}$O, in the energy regime between 100 and 200~MeV projectile kinetic energy, and compare to available data. Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.Comment: 10 pages, 14 figures, 1 tabl

On abrasive water jet machining of miniature brass gears

Abstract: Miniature gears are the key components of various miniaturized devices. Manufacturing quality, surface finish, and surface integrity of miniature gears are of prime importance to determine their functional performance and service life. This article presents the results of some experimental investigations conducted to machine precision miniature brass gears by abrasive water jet machining process. The fabricated gears are external spur type and have 8.4 mm pitch diameter, 12 teeth, and 5 mm thickness. It reports important results i.e. micro‐geometry and surface roughness of miniature gears machined by abrasive water jet process. The manufacturing quality DIN 8 and surface finish 1.03 μm have been obtained in the present research. It also discusses important aspects of various stages of this research along with the discussion on the effects of machining parameters on surface quality of gears, and a detailed surface integrity analysis. The present research identifies AWJM as a sustainable alternate to the conventional processes of miniature gear manufacturing that needs further exploration with other gear types and materials

Investigation on laser beam machining of miniature gears

Abstract: Micro‐machining has become a fast growing field in the global manufacturing sector due to increasing demand of miniature machines and devices. The trend involves the fabrication of precision miniature parts that have widespread applications in many areas such as, electronics, biomedical, aerospace, robotics, automobiles and consumer products. Miniature gears are essential components of miniaturised devices such as miniature motors and pumps, scientific instruments, medical equipment, timing devices, and robots etc. These gears are generally fine‐pitched gears running at very high speed, mainly used for transmission of motion and/or torque. Therefore, minimum running noise, accurate motion transfer and long service life are the required qualities of these gears. Considering that a laser beam is capable of cutting complex shapes with great precision and little waste, motivates its use to machine small sized parts including miniature gears. This article reports on the fabrication of stainless steel miniature gears by laser beam machining (LBM) process. A total of twenty experiments have been conducted following one factor at a time design of experiment strategy on CO2 laser machine. The fabricated gears have 9 mm pitch diameter, 10 teeth, and 4.5 mm thickness. The effects of laser machining parameters on surface roughness (mainly average roughness ‘Ra’ and mean roughness depth ‘Rz’) of gears have been analysed. The best quality miniature gear fabricated by LBM possesses 1.04 μm average roughness and 5.797 μm mean roughness depth at par with that obtained by conventional and other advanced processes of miniature gear manufacturing. Investigation reveals that LBM is capable to produce miniature gears of good surface finish and integrity ensuring their high functional performance and long service life. The outputs of this preliminary work encourage further exploration of LBM to establish it as an alternative process for fabrication of precision miniature gears

Goldstone bosons and a dynamical Higgs field

Higgs inflation uses the gauge variant Higgs field as the inflaton. During inflation the Higgs field is displaced from its minimum, which results in associated Goldstone bosons that are apparently massive. Working in a minimally coupled U(1) toy model, we use the closed-time-path formalism to show that these Goldstone bosons do contribute to the one-loop effective action. Therefore the computation in unitary gauge gives incorrect results. Our expression for the effective action is gauge invariant upon using the background equations of motion.Comment: 27 pages, 2 figures, published version with minor correction

Do Search for Dibaryonic De - Excitations in Relativistic Nuclear Reactions

Some odd characteristics are observed in the single particle distributions obtained from $He + Li$ interactions at $4.5 AGeV/c$ momenta which are explained as the manifestation of a new mechanism of strangeness production via dibaryonic de-excitations. A signature of the formation of hadronic and baryonic clusters is also reported. The di-pionic signals of the dibaryonic orbital de-excitations are analyzed in the frame of the MIT - bag Model and a Monte Carlo simulation.The role played by the dibaryonic resonances in relativistic nuclear collisions could be a significant one. Key words: Relativistic nuclear interactions negative pions, negative kaons, di-pions , streamer chamber, dibaryons, MIT - bag model PACS codes: 25.75.+r,14.40.Aq,14.20.Pt,12.40.AsComment: 17 pages,LATEX, preprint ICTP -243 1993,figures available by reques