Triple Products and Yang-Baxter Equation (I): Octonionic and Quaternionic Triple Systems

We can recast the Yang-Baxter equation as a triple product equation. Assuming the triple product to satisfy some algebraic relations, we can find new solutions of the Yang-Baxter equation. This program has been completed here for the simplest triple systems which we call octonionic and quaternionic. The solutions are of rational type.Comment: 29 page

Endocervical glandular neoplasia associated with lobular endocervical glandular hyperplasia is HPV-independent and correlates with carbonic anhydrase-IX expression: a Gynaecological Oncology Group Study.

BackgroundLobular endocervical glandular hyperplasia (LEGH) is a rare lesion of the uterine cervix. It has been proposed that LEGH may represent a precursor lesion to a group of mucinous adenocarcinoma with gastric phenotype (GA) that is independent of high-risk human papillomavirus (H-HPV) infection. Carbonic anhydrase-IX (CA-IX) is highly expressed in conventional glandular lesions (CGLs). However, expression of CA-IX in LEGH or GA has not been studied.MethodsIn all, 12 CGLs, 7 LEGHs, 6 LEGHs with coexisting adenocarcinoma in situ (AIS, 3) and GA (3) were identified from Japanese women with a cytological diagnosis of atypical glandular cells of undetermined significance. Immunostaining was used to detect CA-IX and p16(INK)4(a) (hereafter termed p16) protein expression in the tissues and CA-IX protein expression in the Papanicolaou smears (PSs). Polymerase chain reaction was used to detect H-HPV DNA in liquid-based cytology.ResultsOut of 12 (83%) CGLs, 10 were positive with H-HPV and high levels of CA-IX expression were seen in all (100%) cases. P16 protein expression was observed in 11 out of 12 (92%) cases. None of the LEGHs, LEGHs with AIS or GA were positive for H-HPV and only 8 out of 13 (62%) showed focal weak (1+) p16 expression. In contrast, all cases (100%) exhibited strong CA-IX protein expression.ConclusionOur study suggests that there are different molecular mechanisms of carcinogenesis resulting in CGLs vs LEGHs associated with AIS or GA. There is also a possible link between LEGHs and GAs. Furthermore, CA-IX expression may serve as a useful biomarker for the detection of GAs in the absence of H-HPV infection

Triple Products and Yang-Baxter Equation (II): Orthogonal and Symplectic Ternary Systems

We generalize the result of the preceeding paper and solve the Yang-Baxter equation in terms of triple systems called orthogonal and symplectic ternary systems. In this way, we found several other new solutions.Comment: 38 page

Josephson π\pi-state in superconductor-Luttinger liquid hybrid systems

Josephson current through a Luttinger liquid (LL) under a magnetic field is theoretically studied. We derive an analytical expression of Josephson current for clean interfaces, by using quasiclassical Green's function and functional bosonization procedure. We show that critical currents can be renormalized by electron-electron interactions at perfect transparency when LL is adiabatically connected with superconductors. We also find that a generation of $\pi$-state, due to spin-dependent energy shift in Andreev bound states (ABS), is prohibited even at zero temperature when the strength of repulsive interactions reaches some critical value. The suppression of $\pi$-state is caused by the low energy fluctuations propagating in LL, and making the Zeeman splitting in ABS blurred.Comment: 5 pages, 4figure

Wave height distribution for plunging breakers induced by air bubbles

Hossain M.N., Araki S., Hoque A., et al. Wave height distribution for plunging breakers induced by air bubbles. Ocean Engineering 309, 118472 (2024); https://doi.org/10.1016/j.oceaneng.2024.118472.This study highlights the wave height distributions based on plunging breaking waves and air bubble effects in the surf zone. Wave height distributions predicted previously by different models have been reformulated in terms of air bubble effects. Some of the most commonly applied wave height distributions are judged using laboratory observations in a custom-built wave flume. Results have revealed a notable deviation from the Rayleigh distribution, with the proposed model demonstrating a closer match to experimental data, particularly for larger wave heights. Probability densities of larger wave heights are reduced significantly by entrained air bubbles, leading to measured wave heights below Rayleigh distribution predictions. In addition, the different wave height parameters derived from the proposed model exhibited good agreement with laboratory data compared to the Rayleigh distribution. Furthermore, theoretical analysis shows the scale parameter's dependence on the decay coefficient, aligning well with measurements and simplifying the proposed distribution to a one-parameter model. Again, based on the error analysis, the proposed model's results show good performance compared to others

Intense pulsed helium droplet beams

Pulsed (30 - 100 microseconds) nozzle beams have been used to generate helium droplets ( = 10^4-10^5). The dependence of the beam intensity and the mean droplet size on the source stagnation pressure and temperature are studied via mass spectroscopy and laser induced fluorescence of embedded phthalocyanine molecules. In comparison to a cw beam the pulsed source for the same pressure and temperature has a factor of 100 higher flux and the droplet sizes are an order of a magnitude larger.Comment: Accepted by Review of Scientific Instrument