The inverse of the metric matrices on the Siegel-Jacobi upper half space ${\mathcal{X}}^J_n$, invariant to the restricted real Jacobi group $G^J_n(\mathbb{R})_0$ and extended Siegel-Jacobi $\tilde {{\mathcal{X}}}^J_n$ upper half space, invariant to the action of the real Jacobi $G^J_n(\mathbb{R})$, are presented. The results are relevant for Berezin quantization of the manifolds ${\mathcal{X}}^J_ n$ and $\tilde {\mathcal{X}}^J_n$. Explicit calculations in the case $n=2$ are given.

This study examines the stability of cosmological models through perturbation theory, focusing on different formulations of the deceleration parameter (DP). By analysing the eigenvalues of perturbations, we identify key insights into the models' long-term dynamics and stability. The results reveal the presence of stable and marginally stable modes, indicating how perturbations evolve and dissipate over cosmic time. These findings provide a deeper understanding of cosmic evolution, the formation of large-scale structures, and the behaviour of perturbations, offering significant contributions to cosmological research and theoretical modelling of the Universe.

We discuss the EPR paradox and study an example of this in a quantum field theoretical context. We show that there is always an alternative description of QFT in which particles that interact at a moment in time remain entangled and therefore in a form of contact at any spatial or temporal separation. Consequently the correlations of spin or other properties of the particles long time after they cease to interact is perfectly natural and justifiable.

With this work our main objective is to find the best general (baseline) model for analyzing unknown spectra using Fourier infrared transformed spectroscopy (FTIR) coupled with machine learning (ML) algorithms. This goal allows us to identify the best methodology applied for inline analysis of different experimental spectra for qualitative structural information obtained with types of structures that generate absorption or emission peaks. This methodology opens new perspectives for automated data processing using flexible algorithms and machine learning to encode experimental data for future applications. The results provide a good perspective on Machine Learning algorithms for applied sciences research. For our case study (FTIR experimental data) our model allows for peak feature extraction with a relative low, close to machine standard deviation, error budget. The best model identified is a specialized model but the standard, fully connected network models are evaluated.

Optical spectroscopic studies of furan molecules (C₄H₄O) impinged by dihydrogen cations (H$_{2}^{+}$) were for the first time performed employing collisioninduced emission spectroscopy at ions incident energy range of 25–1000 eV corresponding to the velocities from 49 to 311 km/s. The recorded spectra reveal strong luminescence of atomic hydrogen Balmer lines whose intensities weaken with rising principal quantum number n. The spectra also display emission bands of CH radicals excited to the first A²Δ and second B²Σ⁻ electronic states. The emission yield curves of these excited products were additionally measured by recording resultant intensities at different projectile energies. Impact processes are unveiled based on these results.

We investigate quantum dynamics for an ion confined within an oscillating quadrupole field, starting from two well known and elegant approaches. It is established that the Hamilton equations of motion, in both Schrödinger and Heisenberg representations, are equivalent to the Hill equation. One searches for a linear independent solution associated to a harmonic oscillator (HO). An adiabatic invariant, which is also a constant of motion, is introduced based on the Heisenberg representation. Thus, the state of the non-autonomous system can be determined at any subsequent moment of time. The quantum states for trapped ions are demonstrated to be Fock (number) states, while the exact solutions of the Schrödinger equation for a trapped ion are exactly the quasienergy states. Semiclassical dynamics is also investigated for many-body systems of trapped ions, where the wavefunction associated to the Schrödinger equation is prepared as a Gauss package multiplied by a Hermite polynomial. We also discuss time evolution for the system under investigation and supply the propagator.

We compute theoretically the loss function in a three layer silicene structure within random phase approximation (RPA) at zero temperature in the homogeneous and inhomogeneous cases. We get analytical expressions for the loss function restricted to the acoustic and optical plasmon branches in the long wavelength approximation. Numerical computations show that as we increase the interlayer distance between the silicene layers the broadened peaks in the loss function associated with the damped plasmons start to merge. Another important effect that we observe numerically is that the plasmonic spectral weight of the loss function associated with undamped plasmonic branches is dominated by the acoustic plasmons.

The simulation of a single pass of equal-channel angular pressing (ECAP) was conducted in the QFORM program. The strain distribution in the longitudinal and transverse sections of a Zr1.0%Nb alloy billet was calculated. This distribution was investigated at various moments $(t_i, i = 1, 2, 3, 4)$ during the shearing deformation in the intersection channels (deformation zone).

The synthesis of some silver nanoparticles was carried out by twostep reduction, with chemical or biological antioxidants, and subsequent exposure to ultraviolet radiation. Synthesis efficiency was progressively increased after 30 min during second step: about 40% increase of LSPR band intensity for chemical reducing and more than 100% enhancing for biological reducing.

In this paper, we propose for the first time to the best of our knowledge, extend the application of a stochastic Eulerian numerical approach based on the Extended Kalman Filter (EKF_E.N.M.) to address the limitations of the Eulerian air pollution model CHIMERE. This approach integrates a comprehensive set of processes, including advection, turbulence, chemical reactions, emissions, and deposition, to model the dynamics of pollutant mass concentration. The EKF technique is employed to transform nonlinear dynamic problems into a succession of locally linearized ones, which are then used to estimate system states and adjust pollutant concentrations based on measured data. This stochastic approach is tested through two scenarios: one without external forces or control terms, and another that incorporates external factors like temperature, wind speed, and nitrogen dioxide as ozone precursors. A comparison of the obtained results with those from the standard CHIMERE model and studies from the literature demonstrates the accuracy and effectiveness of the proposed method.

Against the backdrop of global warming and the necessary reduction of CO₂, the material wood is experiencing a renaissance as a result of increasing social acceptance. However, questions of harmless reforestation also come to the forefront. Ultimately, plantation cultivation of wood is unavoidable in order to meet the increasing demand for wood in the coming years. Agroforestry is the focus of economic and technical interest in this regard.
Paulownia or Kiri tree belongs to the Paulowniaceae family and is the tree with the highest growth rate in the world. It has a large leaf area that can absorb correspondingly high amounts of CO₂. Originally from China, it is now planted worldwide and is considered a climate tree. However, it must face the accusation of invasiveness. Therefore, less invasive varieties of Paulownia are of interest. However, these should also have appropriate mechanical properties. One of these material properties is damping, which significantly affects the acoustic behaviour.
In this study, the strain-dependent damping was investigated by measuring the logarithmic decrement of free decaying bending oscillations. The measurements were carried out on a common Paulownia species (obtained from plantations in Georgia, Italy and Spain) and a new species of Paulownia obtained from a plantation in Germany. It is worth mentioning that the new wood variety was harvested for the first time in Germany.
Since damping is strongly influenced by microstructure, which is in turn influenced by site-specific nutrient supply, this study examined how damping behaviour develops with strain and the extent of its variation. It was found that the damping curves exhibited a strain-independent and a strain-dependent area. The bending modulus was calculated from the oscillation frequency and showed that the values range from about 1024 N/mm² to 5873 N/mm². This large variation appears to stem from the fiber orientation of the tested samples, which also affects the damping values.

In this paper we present the effects of fringing on the measurement of the tip-sample capacitance for Kelvin probes driven by a harmonic backing potential. Moreover, we show that in this case it is still possible to obtain good estimations of operational parameters that allow for the fully controlled operation of harmonically driven Kelvin probes.