Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.     

A Weighted Trudinger–Moser Inequality on R^N and Its Application to Grushin Operator

Let x=(x',x')with x'∈Rk and x'∈R^N-k andΩbe a x'-symmetric and bounded domain in R^N(N≥2).We show that if 0≤a≤k-2,then there exists a positive constant C>0 such that for all x'-symmetric function u∈C0^∞(Ω)with∫Ω|■u(x)|^N-a|x'|^-adx≤1,the following uniform inequality holds1/∫Ω|x|^-adx∫Ωe^βa|u|N-a/N-a-1|x'|^-adx≤C,whereβa=(N-a)(2πN/2Γ(k-a/2)Γ(k/2)/Γ(k/2)r(N-a/2))1/N-a-1.Furthermore,βa can not be replaced by any greater number.As the application,we obtain some weighted Trudinger–Moser inequalities for x-symmetric function on Grushin space.     

Sterically Facilitated Intramolecular Nucleophilic NMe2 Group Substitution in the Synthesis of Fused Isoxazoles: Theoretical Study

The influence of steric repulsion between the NMe₂ group and a second ortho-(peri-)substituent in the series of 1-dimethylaminonaphthalene and N,N-dimethylanilene ortho-oximes on the ease of the NMe₂ group’s intramolecular nucleophilic substitution is studied. Possible reaction intermediates for three mechanisms are calculated (ωB97xd/def-2-TZVP), and their free Gibbs energies are compared to model reaction profiles. Supporting experiments have proved the absence of studied reactivity in the case of simple 2-dimethylaminobenzaldoxime, which allowed us to establish reactivity limits. The significant facilitation of NMe₂ group displacement in the presence of bulky substituents is demonstrated. The possibility of fused isoxazoles synthesis via the intramolecular nucleophilic substitution of a protonated NMe₂ group in the aniline and naphthalene series is predicted.     

Physical,Thermal and Biological Properties of Yellow Dyes with Two Azodiphenylether Groups of Anthracene

Two yellow bis-azo dyes containing anthracene and two azodiphenylether groups (BPA and BTA) were prepared, and an extensive investigation of their physical, thermal and biological properties was carried out. The chemical structure was confirmed by the FTIR spectra, while from the UV–Vis spectra, the quantum efficiency of the laser fluorescence at the 476.5 nm was determined to be 0.33 (BPA) and 0.50 (BTA). The possible transitions between the energy levels of the electrons of the chemical elements were established, identifying the energies and the electronic configurations of the levels of transition. Both crystals are anisotropic, the optical phenomenon of double refraction of polarized light (birefringence) taking place. Images of maximum illumination and extinction were recorded when the crystals of the bis-azo compounds rotated by 90° each, which confirms their birefringence. A morphologic study of the thin films deposited onto glass surfaces was performed, proving the good adhesion of both dyes. By thermal analysis and calorimetry, the melting temperatures were determined (~224–225 °C for both of them), as well as their decomposition pathways and thermal effects (enthalpy variations during undergoing processes); thus, good thermal stability was exhibited. The interaction of the two compounds with collagen in the suede was studied, as well as their antioxidant activity, advocating for good chemical stability and potential to be safely used as coloring agents in the food industry.     

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.