Tissue-like phantoms are widely used as a model for mimicking the optical properties of live tissue. This paper presents the results of a diffusion reflection method as well as fluorescence lifetime imaging microscopy measurements of fluorescein-conjugated gold nanorods in solution as well as inserted in solid tissue-imitating phantoms. A lack of consistency between the fluorescence lifetime results of the solutions and the phantoms raises a question about the ability of tissue-like phantoms to maintain the optical properties of inserted contrast agents.

The paper is a continuation of another paper (https://philpapers.org/rec/PENFLT-2) published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The relevant mathematical structure is Hilbert arithmetic in a wide sense (https://dx.doi.org/10.2139/ssrn.3656179), in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem.

Background: In this study, we aimed to evaluate the effect of s-FLT-1 and PlGF concentrations in women in the first trimester of pregnancy on the pulsatility index of the ductus venosus and the right and left uterine arteries. Methods: A total of 108 pregnant women in their first trimester were included in the study, with 87 assigned to the experimental group and 21 to the control group. Ultrasound examination were performed to measure the uterine artery pulsatility index, resistance index, ductus venosus pulsatility index, and blood sampling levels of biomarkers such as b-HCG; PAPP-A; s-FLT-1 and PlGF. Results: There was a significant negative relationship between PAPP-A concentration and the risk of fetal growth restriction, and a significant negative relationship between PlGF concentration and the risk of preeclampsia and fetal growth restriction in women in their first trimester of pregnancy. There was also a significant positive relationship between sFLT-1/PLGF ratio and the risk of developing preeclampsia. No significant relationships were found between the concentrations of biomarkers beta-HCG, PAPP-A, sFLT-1, PlGF, and any of the parameters PIUARt, PIUALt, Mean uterine arteries, and DVPI. Summary: In conclusion, this study did not find conclusive evidence to support the hypothesis that beta-HCG, PAPP-A, s-FLT-1, and PlGF concentrations in women in the first trimester of pregnancy have a significant effect on the Pulsatility Index of the ductus venosus and the Right and left Uterine Arteries. Further research is needed to investigate these potential associations.