Central limit theorem for intrinsic Fréchet means in smooth compact Riemannian manifolds. - In: Probability theory and related fields, ISSN 1432-2064, Bd. 0 (2024), 0, insges. 28 S.
We prove a central limit theorem (CLT) for the Fréchet mean of independent and identically distributed observations in a compact Riemannian manifold assuming that the population Fréchet mean is unique. Previous general CLT results in this setting have assumed that the cut locus of the Fréchet mean lies outside the support of the population distribution. In this paper we present a CLT under some mild technical conditions on the manifold plus the following assumption on the population distribution: in a neighbourhood of the cut locus of the population Fréchet mean, the population distribution is absolutely continuous with respect to the volume measure on the manifold and in this neighhbourhood the Radon-Nikodym derivative has a version that is continuous. So far as we are aware, the CLT given here is the first which allows the cut locus to have co-dimension one or two when it is included in the support of the distribution. A key part of the proof is establishing an asymptotic approximation for the parallel transport of a certain vector field. Whether or not a non-standard term arises in the CLT depends on whether the co-dimension of the cut locus is one or greater than one: in the former case a non-standard term appears but not in the latter case. This is the first paper to give a general and explicit expression for the non-standard term which arises when the co-dimension of the cut locus is one.
https://doi.org/10.1007/s00440-024-01291-3
Tailoring phosphine ligands for improved C-H activation: insights from Δ-machine learning. - In: Digital discovery, ISSN 2635-098X, Bd. 0 (2024), 0, insges. 15 S.
Transition metal complexes have played crucial roles in various homogeneous catalytic processes due to their exceptional versatility. This adaptability stems not only from the central metal ions but also from the vast array of choices of the ligand spheres, which form an enormously large chemical space. For example, Rh complexes, with a well-designed ligand sphere, are known to be efficient in catalyzing the C-H activation process in alkanes. To investigate the structure-property relation of the Rh complex and identify the optimal ligand that minimizes the calculated reaction energy ΔE of an alkane C-H activation, we have applied a Δ-machine learning method trained on various features to study 1743 pairs of reactants (Rh(PLP)(Cl)(CO)) and intermediates (Rh(PLP)(Cl)(CO)(H)(propyl)). Our findings demonstrate that the models exhibit robust predictive performance when trained on features derived from electron density (R2 = 0.816), and SOAPs (R2 = 0.819), a set of position-based descriptors. Leveraging the model trained on xTB-SOAPs that only depend on the xTB-equilibrium structures, we propose an efficient and accurate screening procedure to explore the extensive chemical space of bisphosphine ligands. By applying this screening procedure, we identify ten newly selected reactant-intermediate pairs with an average ΔE of 33.2 kJ mol−1, remarkably lower than the average ΔE of the original data set of 68.0 kJ mol−1. This underscores the efficacy of our screening procedure in pinpointing structures with significantly lower energy levels.
https://doi.org/10.1039/D4DD00037D
Quantum particle under dynamical confinement: from quantum fermi acceleration to high harmonic generation. - In: Physica scripta, ISSN 1402-4896, Bd. 99 (2024), 7, 075308, S. 1-13
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely time-varying external potential is treated by obtaining exact solution. Also, some external potentials approving separation of space and time variables in the Schrödinger equation with time-dependent boundary conditions are classified. Time-dependence of the average kinetic energy and average quantum force are analyzed. A model for optical high harmonic generation in the presence of dynamical confinement and external monochromatic time-dependent homogeneous electric field is proposed.
https://doi.org/10.1088/1402-4896/ad52c8
Perturbation and spectral theory for singular indefinite Sturm-Liouville operators. - In: Journal of differential equations, ISSN 1090-2732, Bd. 405 (2024), S. 151-178
https://doi.org/10.1016/j.jde.2024.05.043
C60 fullerene reduces the level of liver damage in chronic alcohol intoxication of rats. - In: Molecules, ISSN 1420-3049, Bd. 29 (2024), 13, 2951, S. 1-15
The liver is the main organ responsible for the metabolism of ethanol, which suffers significantly as a result of tissue damage due to oxidative stress. It is known that C60 fullerenes are able to efficiently capture and inactivate reactive oxygen species in in vivo and in vitro systems. Therefore, the purpose of this study is to determine whether water-soluble C60 fullerene reduces the level of pathological process development in the liver of rats induced by chronic alcohol intoxication for 3, 6, and 9 months, depending on the daily dose (oral administration; 0.5, 1, and 2 mg/kg) of C60 fullerene throughout the experiment. In this context, the morphology of the C60 fullerene nanoparticles in aqueous solution was studied using atomic force microscopy. Such biochemical parameters of experimental animal blood as ALT (alanine aminotransferase), AST (aspartate aminotransferase), GGT (gamma-glutamyl transferase) and ALP (alkaline phosphatase) enzyme activities, CDT (carbohydrate-deficient transferrin) level, values of pro-antioxidant balance indicators (concentrations of H2O2 (hydrogen peroxide) and GSH (reduced glutathione), activities of CAT (catalase), SOD (superoxide dismutase) and GPx (selenium-dependent glutathione peroxidase)), and pathohistological and morphometric features of liver damage were analyzed. The most significant positive change in the studied biochemical parameters (up to 29 ± 2% relative to the control), as markers of liver damage, was recorded at the combined administration of alcohol (40% ethanol in drinking water) and water-soluble C60 fullerenes in the optimal dose of 1 mg/kg, which was confirmed by small histopathological changes in the liver of rats. The obtained results prove the prospective use of C60 fullerenes as powerful antioxidants for the mitigation of pathological conditions of the liver arising under prolonged alcohol intoxication.
https://doi.org/10.3390/molecules29132951
Port-Hamiltonian descriptor systems are relative generically controllable and stabilizable. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 0 (2024), 0, insges. 37 S.
The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359-377, 2021) on generic controllability and of Ilchmann and Kirchhoff (Math Control Signals Syst 35:45-76, 2022) on relative generic controllability of linear differential-algebraic equations. We extend the result from general, unstructured differential-algebraic equations to differential-algebraic equations of port-Hamiltonian type. We derive results on relative genericity. These findings are the basis for characterizing relative generic controllability of port-Hamiltonian systems in terms of dimensions. A similar result is proved for relative generic stabilizability.
https://doi.org/10.1007/s00498-024-00392-7
FCF-LDH/BiVO4 with synergistic effect of physical enrichment and chemical adsorption for efficient reduction of nitrate. - In: Green energy & environment, ISSN 2468-0257, Bd. 9 (2024), 7, S. 1112-1121
Photoelectrochemical NO3− reduction (PEC NITRR) not only provides a promising solution for promoting the global nitrogen cycle, but also converts NO3− to the important chemicals (NH3). However, it is still a great challenge to prepare catalysts with excellent NO3− adsorption/activation capacity to achieve high NITRR. Herein, we designed a novel Fe2+Cu2+Fe3+LDH/BiVO4 (FCF-LDH/BVO) catalyst with synergistic effect of chemical adsorption and physical enrichment. Fe2+ in FCF-LDH/BVO provides the rich Lewis acid sites for the adsorption of NO3−, and the appropriate layer spacing of FCF-LDH further promotes the physical enrichment of NO3− in its interior, thus realizing the effective contact between NO3− and active sites (Fe2+). FCF-LDH/BVO showed excellent NH3 production performance (FENH3 = 66.1%, rNH3 = 13.8 μg h−1 cm−2) and selectivity (FENO2- = 2.5%, rNO2- = 4.9 μg h−1 cm−2) in 0.5 mol L−1 Na2SO4 electrolyte. In addition, FCF-LDH/BVO maintains the desirable PEC stability for six cycle experiments, showing great potential for practical application. The 14NO3− and 15NO3− isotope test provides strong evidence for further verification of the origin of N in the generated NH3. This LDH catalyst has a great potential in PEC removal of NO3− from groundwater.
https://doi.org/10.1016/j.gee.2023.05.011
Effect of orbital symmetry on probing the single-molecule Kondo effect. - In: Physical review, ISSN 2469-9969, Bd. 109 (2024), 24, L241401, S. L241401-1-L241401-6
The low-energy excitation spectrum of a metal-free phthalocyanine molecule on Ag(111) is probed in scanning tunneling spectroscopy experiments. The use of functionalized p-orbital and s-orbital tips leads to markedly different results. While CO-terminated p-wave tips probe the zero-energy Abrikosov-Suhl resonance induced by the molecular Kondo effect, Ag-coated s-wave tips - in strong contrast - feign the absence of the Kondo effect due to a missing Abrikosov-Suhl resonance. Reducing the vertical distance between the s-orbital tip and the molecule progressively unveils the resonance, compatible with findings for the p-orbital tip in the far tunneling range. A mechanism based on orbital overlap is suggested as the tentative origin of the observations. The CO-functionalized tip is then used to explore the altered Kondo effect of the tautomerized phthalocyanine.
https://doi.org/10.1103/PhysRevB.109.L241401
Funnel MPC for nonlinear systems with arbitrary relative degree. - In: Automatica, ISSN 0005-1098, Bd. 167 (2024), 111759, S. 1-10
The model predictive control (MPC) scheme funnel MPC enables output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Earlier works achieved the control objective for system with relative degree restricted to one or incorporated additional feasibility constraints in the optimal control problem. Here we resolve these limitations by introducing a modified stage cost function relying on a weighted sum of the tracking error derivatives. The weights need to be sufficiently large and we state explicit lower bounds. Under these assumptions we are able to prove initial and recursive feasibility of the novel funnel MPC scheme for systems with arbitrary relative degree - without requiring any terminal conditions, a sufficiently long prediction horizon or additional output constraints.
https://doi.org/10.1016/j.automatica.2024.111759
Investigation of Tl-doped silicon by low-temperature photoluminescence during light-induced degradation treatments. - In: Physica status solidi, ISSN 1862-6319, Bd. n/a (2024), n/a, 2400287, S. 1-6
Scientific progress is made in understanding photoluminescence (PL) lines in thallium-doped silicon. Two PL lines called A and P, which appear after quenching, are found to exhibit irreversible as well as reversible behavior under the application of light-induced degradation (LID) treatments. The reversible behavior is similar to changes of a P line in indium-doped silicon due to LID treatments, which have led to the identification of this P line to be caused by an InSi-Sii-defect. By exploiting the metastability of defects from the ASi-Sii category, the experimental findings of this study indicate that the underlying defect for the A and P line in thallium-doped silicon is the TlSi-Sii-defect.
https://doi.org/10.1002/pssa.202400287