A classification of plane and planar 2-trees

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.Comment: 26 pages, 14 figure

Shuffle operations on discrete paths

AbstractWe consider the shuffle operation on paths and study some parameters. In the case of square lattices, shuffling with a particular periodic word (of period 2) corresponding to paperfoldings reveals some characteristic properties: closed paths remain closed; the area and perimeter double; the center of gravity moves under a 45∘ rotation and a 2 zoom factor. We also observe invariance properties for the associated Dragon curves. Moreover, replacing square lattice paths by paths involving 2kπ/N-turns, we find analogous results using more general shuffles

The collaborative process of sustainable innovations under the lens of actor–network theory

The development of sustainable innovation (SI) is complex and risky due to the characteristics and diversity of actors involved in its process. Little is known about the collaborative process underlying this development. The objective of the paper is to explore the collaborative mechanisms and dynamics that influence the process and characteristics of sustainable innovations. The translation approach of the actor–network theory is applied to shed light on the collaborative process of two cases of sustainable innovations within small-and medium-sized enterprises. The sociotechnical graph method is used as a methodology to track the mechanisms and compare the dynamics of their processes. The results reveal that the governance characteristic of sustainable innovations and the moment of mobilization are essential aspects of the collaborative processes. They show that, depending on the intensity and systemic impacts of SI, attraction and retention are important mechanisms in the construction of the governance characteristics of SI. A manager who uses these mechanisms during the mobilization of actors, having resources related to the governance characteristics, succeeds in sustainable innovation development. The paper contributes to the literature on sustainability management by linking the ‘becoming’ of sustainable innovations to their collaborative processes. It also informs managers on how to manage the collaborative process of sustainable innovations by relying on a translation approach. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Breit Hamiltonian and QED Effects for Spinless Particles

We describe a simplified derivation for the relativistic corrections of order $\alpha^4$ for a bound system consisting of two spinless particles. We devote special attention to pionium, the bound system of two oppositely charged pions. The leading quantum electrodynamic (QED) correction to the energy levels is of the order of $\alpha^3$ and due to electronic vacuum polarization. We analyze further corrections due to the self-energy of the pions, and due to recoil effects, and we give a complete result for the scalar-QED leading logarithmic corrections which are due to virtual loops involving only the scalar constituent particles (the pions); these corrections are of order $\alpha^5 \ln \alpha$ for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press

The Single Photon Annihilation Contributions to the Positronium Hyperfine Splitting to Order meα6m_e\alpha^6

The single photon annihilation contributions for the positronium ground state hyperfine splitting are calculated analytically to order $m_e\alpha^6$ using NRQED. Based on intuitive physical arguments the same result can also be determined by a trivial calculation using results from existing literature. Our result completes the hyperfine splitting calculation to order $m_e\alpha^6$. We compare the theoretical prediction with the most recent experimental measurement.Comment: 8 pages, latex, two eps figures include

Searching for New Physics in Leptonic Decays of Bottomonium

New Physics can show up in various well-known processes already studied in the Standard Model, in particular by modifying decay rates to some extent. In this work, I examine leptonic decays of $\Upsilon$ vector resonances of bottomonium below $B\bar{B}$ production, subsequent to a magnetic dipole radiative structural transition of the vector resonance yielding a pseudoscalar continuum state, searching for the existence of a light Higgs-like neutral boson that would imply a slight but experimentally measurable breaking of lepton universality.Comment: LaTeX, 12 pages, 1 EPS figur

Biomechanical effect of pedicle screw distribution in AIS instrumentation using a segmental translation technique: computer modeling and simulation

BACKGROUND: Efforts to select the appropriate number of implants in adolescent idiopathic scoliosis (AIS) instrumentation are hampered by a lack of biomechanical studies. The objective was to biomechanically evaluate screw density at different regions in the curve for AIS correction to test the hypothesis that alternative screw patterns do not compromise anticipated correction in AIS when using a segmental translation technique. METHODS: Instrumentation simulations were computationally performed for 10 AIS cases. We simulated simultaneous concave and convex segmental translation for a reference screw pattern (bilateral polyaxial pedicle screws with dorsal height adjustability at every level fused) and four alternative patterns; screws were dropped respectively on convex or concave side at alternate levels or at the periapical levels (21 to 25% fewer screws). Predicted deformity correction and screw forces were compared. RESULTS: Final simulated Cobb angle differences with the alternative screw patterns varied between 1 degrees to 5 degrees (39 simulations) and 8 degrees (1 simulation) compared to the reference maximal density screw pattern. Thoracic kyphosis and apical vertebral rotation were within 2 degrees of the reference screw pattern. Screw forces were 76 +/- 43 N, 96 +/- 58 N, 90 +/- 54 N, 82 +/- 33 N, and 79 +/- 42 N, respectively, for the reference screw pattern and screw dropouts at convex alternate levels, concave alternate levels, convex periapical levels, and concave periapical levels. Bone-screw forces for the alternative patterns were higher than the reference pattern (p 0.28). Alternate dropout screw forces were higher than periapical dropouts (p < 0.05). CONCLUSIONS: Using a simultaneous segmental translation technique, deformity correction can be achieved with 23% fewer screws than maximal density screw pattern, but resulted in 25% higher bone-screw forces. Screw dropouts could be either on the convex side or on the concave side at alternate levels or at periapical levels. Periapical screw dropouts may more likely result in lower bone-screw force increase than alternate level screw dropouts

Relativistic and Binding Energy Corrections to Direct Photon Production In Upsilon Decay

A systematic gauge-invariant method is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v^2) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.Comment: 13 pages, LateX, One figure (to be published in Phys. Rev. D, Sept. 1, 1996

Adaptive soundscape design for liveable urban spaces: a hybrid methodology across environmental acoustics and sonic art

The aim of this research is to identify and implement soundscape improvement strategies in urban areas based on loudspeaker placements in the outdoor environment and the use of a computer-based system for adaptive soundscape generation, integrating sonic art practice with acoustic engineering rigour

Cusps in K --> 3 pi decays

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl