On the Identity of Some von Neumann Algebras and Some Consequences

Among von Neumann algebras, the Weyl algebra W{\mathcal{W}} generated by two unitary groups {U(α)} and {V(β)}, the algebra U{\mathcal{U}} generated by a completely non-unitary semigroup of isometries {U ₊(α)} and the Weyl algebra W₊^h{\mathcal{W}_{+}^{h}} pertaining to a semi-bounded space with homogeneous spectrum of the generator of {V(β)}, all share the property that their representations are completely reducible and the irreducible representations are equivalent. We trace this fact to the identity of these algebras, in the sense that any of them contains a representation of any of the remaining two algebras, which in turn contains the original algebra. We prove this statement by explicit construction. The aforementioned results about the representations of the algebras follow immediately from the proof for any of them. Also, by the above construction we prove for W^h₊{\mathcal{W}^{h}_{+}} the analog of a theorem by Sinai for W{\mathcal{W}} : given {V(β)} with semi-bounded homogeneous spectrum, there exists a completely non-unitary semigroup {U ₊(α)} such that {V(β)} and {U ₊(α)} generate W₊^h{\mathcal{W}_{+}^{h}}.     

Use of generalized exponential function to build three-dimensional reactive surfaces

In this work, we introduce a new analytical form based on the q-exponential function to build three-dimensional reactive surfaces. The quality of this new function is tested by fitting the ab initio potential energy surface (PES) to the ground state Na+HF reaction. The thermal rate constant and reactive probabilities were determined considering this new PES. The obtained properties agree with those found for other PES available in literature.     

Is Teleparallel Gravity Really Equivalent to General Relativity?

An axiomatization of the so‐called Teleparallel Equivalent to General Relativity is presented. A set of formal and semantic postulates are elaborated from where the physical meaning of various key concepts of the theory are clarified. These concepts include those of inertia, Lorentz and diffeomorphism invariance, and reference frame. It is shown that Teleparallel Gravity admits a wider representation of space‐time than General Relativity, allowing to define properties of the gravitational field such as energy and momentum that are usually considered problematic. In this sense, although the dynamical equations of both theories are equivalent, their inequivalence from a physical point of view is demonstrated. Finally, the axiomatic formulation is used to compare Teleparallel Gravity with other theories of gravity based on absolute parallelism such as non‐local and f(T) gravity.     

Predictive model for the collapse load of masonry assemblage with two piers joined by a spandrel

The masonry assemblage composed of two piers connected by a spandrel can be considered a repetitive unit in large masonry walls with openings, occurring in masonry buildings. In this work, the collapse load of the above-mentioned masonry assemblage is predicted by solving a system of nonlinear equations, where the normal force in the spandrel is a root of an equilibrium equation of fourth degree. Piers and spandrel are assumed rigid and nonlinearity (crushing and no tensile strength) is concentrated at the pier-foundation and pier–spandrel interfaces. The model also takes into account the effect of a timber lintel supporting the spandrel and anchored into the two adjacent piers. This approach valid for assemblages with one spandrel can be extended for the evaluation of the collapse load of structures composed of N piers connected by N ? 1 spandrels. The system of nonlinear equations is easily solved with an iterative method and the collapse load provided by the solution agrees well with the experimental result.     

Harnessing Greenhouse Gases Absorption by Doped Fullerenes with Externally Oriented Electric Field

In this work, a theoretical investigation of the effects caused by the doping of C₂₀ with silicon (Si) atom as well as the adsorption of CO, CO₂ and N₂ gases to C₂₀ and C₁₉Si fullerenes was carried out. In concordance with previous studies, it was found that the choice of the doping site can control the structural, electronic, and energetic characteristics of the C₁₉Si system. The ability of C₂₀ and C₁₉Si to adsorb CO, CO₂ and N₂ gas molecules was evaluated. In order to modulate the process of adsorption of these chemical species to C₁₉Si, an externally oriented electric field was included in the theoretical calculations. It was observed that C₁₉Si is highly selective with respect to CO adsorption. Upon the increase of the electric field intensity the adsorption energy was magnified correspondingly and that the interaction between CO and C₁₉Si changes in nature from a physical adsorption to a partial covalent character interaction.     

Visible-Light Promoted Intramolecular para-Cycloadditions on Simple Aromatics

Dearomative cycloadditions are a powerful tool to access a large chemical space exploiting simple and ubiquitous building blocks. The energetic burden due to the loss of aromaticity has however greatly limited their synthetic potential. We devised a general intramolecular method that overcomes these limitations thanks to the photosensitization of allenamides. The visible-light-promoted process gives complex [2.2.2]-(hetero)-bicyclooctadienes at room temperature, likely through the stabilization of transient (bi)radicals by naphthalene. The reaction tolerates several valuable functionalities, offering a convenient handle for a myriad of applications, including original isoindoles and metal complexes.     

Flame surface modification of polyethylene sheets

High density polyethylene sheets 2 mm thick were flame treated to modify the surface properties. Sheets treated using a flame with air to gas (methane) ratio ∼ 10:1 at different distances between the inner cone tip of the flame and the polymer surface were investigated. Grafting of selected monomers as maleic anhydride, acrylamide and glycidyl methacrylate was attempted by flame treatment of sheets covered with a monomer layer. Good grafting results were obtained with acrylamide and maleic anhydride. The surface temperature-time dependence during the flame treatment was measured with a high resolution thermocouple. Scanning Electron Microscopy (SEM) allowed evidencing a modified thickness of about 120 μ. The chemical surface modification was studied by X ray Photoelectron Spectroscopy (XPS) and Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFT). The hydroxyl, carbonyl and carboxyl content was measured after derivatization with reagents containing an elemental tag to facilitate XPS analysis of surface functional groups. In comparison to the untreated polyethylene, wetting tension and contact angle of the flamed materials showed a strong variation. This variation was almost independent of the distance between the flame and the polymer surface. Adhesion between treated polyethylene and a polyurethane adhesive was determined using T-peel test measurements. High adhesion levels were found with flame treated polyethylene at 5 mm distance. XPS results indicate that when adhesion is high, the hydroxyl is in excess compared to the other measured functions, i.e. carbonyl and carboxyl species.     

Molecular dynamics simulation of semirigid polymers

The chain rigidity of poly(p-hydroxybenzoate) was estimated through the theoretical evaluation of its persistence length (L_p). A non-Brownian molecular dynamics (MD) simulation of an isolated chain with 20 monomeric units was performed. The sampled conformational population was analyzed and the orientational correlation function between monomeric units along the chain was calculated. An algorithm based on the worm-like chain model was applied to evaluate the persistence length. The results were compared with those obtained from equilibrium models like the freely-rotating-chain and the rotational-matrix method with fluctuations. Equilibrium models give different results depending on the degree of accuracy used in describing the monomeric unit. The inclusion of thermal fluctuations is crucial to obtain realistic results. These coincide with those given by MD simulation when only nearest-neighbour orientational correlations are taken into account: inclusion of higher-order correlation terms leads to lower values of the persistence length. The origin of this discrepancy was investigated. The MD simulation results are characterized by an overrepresentation of conformations with a short end-to-end distance resulting from an anomalous energy concentration in the first bending mode of the chain. In analogy with previous simulation results from systems characterized by a week coupling amoung their degrees of freedom, failure in the energy equipartition is proposed as a likely explanation of the anomalous dynamical behaviour.