On Solutions of a Nonlinear Erdélyi-Kober Integral Equation

We conduct some investigations concerning the solvability of a nonlinear integral equation of Erdélyi-Kober type. To facilitate our study we will first consider a nonlinear integral equation of Volterra-Stieltjes type. Since the mentioned Erdélyi-Kober integral equation turns out to be a special case of that of Volterra-Stieltjes type, we can apply the obtained results to the Erdélyi-Kober integral equation. Examples illustrating the obtained results will be also included

Macro-GH - a clinical entity causing a diagnostic challenge - a case report.

AIM: Presentation of a new case of a patient with macro-GH, that may interfere with different GH assays leading to false-positive results in serum samples. CASE PRESENTATION: A 61-year-old female was referred with a pituitary macroadenoma and elevated growth hormone levels The laboratory tests showed increased fasting GH level, measured by a sandwich chemiluminescence immunoassay (LIAISON® XL) without suppression on oral glucose tolerance test and normal IGF-1. The patient did not have the typical signs and symptoms of acromegaly. The patient underwent a transsphenoidal resection of a pituitary tumor, showing only α-subunit immunostaining. Postoperative GH levels remained elevated. An interference in the determination of GH level was suspected. GH was analyzed by three different immunoassays, UniCel DxI 600, Cobas e411 and hGH-IRMA. Heterophilic antibodies and rheumatoid factor were not detected in serum sample. GH recovery after precipitation with 25% polyethylene glycol (PEG) was 12%. Size-exclusion chromatography confirmed the presence of macro-GH in serum sample. CONCLUSION: If results of laboratory tests are not consistent with the clinical findings, the presence of an interference within immunochemical assays could be suspected. To identify interference caused by the macro-GH, the PEG method and size-exclusion chromatography should be used

The basic propositions on defect numbers, root numbers and indices of linear operators

Abstract: In this work, we use the notion of the measure of noncompactness in order to establish some results concerning the class of semi-Fredholm and Fredholm operators. Further, we apply the results we obtained to prove the invariance of the Schechter essential spectrum on Banach spaces by means of polynomially compact perturbations

Hypersatellite x-ray decay of 3d3d hollow-KK-shell atoms produced by heavy-ion impact

We report on the radiative decay of double K-shell vacancy states produced in solid Ca, V, Fe, and Cu targets by impact with about 10 MeV/amu C and Ne ions. The resulting K hypersatellite x-ray emission spectra were measured by means of high- energy-resolution spectroscopy using a von Hamos bent crystal spectrometer. The experiment was carried out at the Philips variable energy cyclotron of the Paul Scherrer Institute. From the fits of the x-ray spectra the energies, line widths, and relative intensities of the hypersatellite x-ray lines could be determined. The fitted intensities were corrected to account for the energy-dependent solid angle of the spectrometer, effective source size, target self-absorption, crystal reflectivity, and detector efficiency. The single-to-double K-shell ionization cross-section ratios were deduced from the corrected relative intensities of the hypersatellites and compared to theoretical predictions from the semiclassical approximation model using hydrogenlike and Dirac-Hartree-Fock wave functions and from classical trajectory Monte Carlo calculations

Testing quantum electrodynamics in extreme fields using helium-like uranium

Funding Information: The results presented here are based on the experiment E125, which is performed at the infrastructure ESR at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, in the framework of FAIR Phase-0 and SPARC collaboration. This work is supported by the Horizon 2020 research and innovation programme of the European Union and grant agreement no. 6544002. We acknowledge the support provided by ErUM FSP T05-‘Aufbau von APPA bei FAIR’ (BMBF nos. 05P19SJFAA and 05P21SJFA1). We thank A. Malyshev, V. Shabaev and Y. Kozhedub for providing previously unknown theoretical results and also for the discussions on theoretical uncertainties. M.T. thanks the ExtreMe Matter Institute EMMI and Alexander von Humboldt Foundation for their support for the stays at the GSI for the preparation and data acquisition. L.D. acknowledges funding support from the Initiative Physique des Infinis (IPI), a research training programme of the Idex SUPER at Sorbonne Université. Funding Information: The results presented here are based on the experiment E125, which is performed at the infrastructure ESR at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, in the framework of FAIR Phase-0 and SPARC collaboration. This work is supported by the Horizon 2020 research and innovation programme of the European Union and grant agreement no. 6544002. We acknowledge the support provided by ErUM FSP T05-‘Aufbau von APPA bei FAIR’ (BMBF nos. 05P19SJFAA and 05P21SJFA1). We thank A. Malyshev, V. Shabaev and Y. Kozhedub for providing previously unknown theoretical results and also for the discussions on theoretical uncertainties. M.T. thanks the ExtreMe Matter Institute EMMI and Alexander von Humboldt Foundation for their support for the stays at the GSI for the preparation and data acquisition. L.D. acknowledges funding support from the Initiative Physique des Infinis (IPI), a research training programme of the Idex SUPER at Sorbonne Université. Publisher Copyright: © 2024, The Author(s).Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions 1–6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron–electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s 1/22p 3/2 J = 2 → 1s 1/22s 1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron–electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.publishersversionpublishe