Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

Enhancement of optical gain and amplified spontaneous emission due to waveguide geometry in the conjugated polymer poly[2-methoxy-5-(2′-ethylhexyloxy)-p-phenylene vinylene]

We report enhanced amplified spontaneous emission (ASE) and optical gain performance in a conjugated polymer (CP)-based thin film waveguide (WG) Si(100)/SiO2/poly[2-methoxy-5-(2′-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV) by encapsulating the active layer with a transparent dielectric film of poly(methyl methacrylate) (PMMA). With index matched SiO2 and PMMA claddings, symmetric WGs are formed that exhibit increased mode confinement and reduced propagation loss enabling lower ASE threshold (40%) and higher optical gain (50%) compared to Si(100)/SiO2/MEH-PPV/air asymmetric WGs. An extremely large net gain coefficient of 500 cm−1 is achieved under picosecond pulse excitation, which is >4× larger than values previously reported in the literature. Fabrication of symmetric WGs requires no complex processing techniques, thus offering a simple, low-cost approach for effectively controlling the ASE behavior of CP-based WGs and related optical devices

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page

Concerted electron-proton transfer in the optical excitation of hydrogen-bonded dyes

The simultaneous, concerted transfer of electrons and protons—electron-proton transfer (EPT)—is an important mechanism utilized in chemistry and biology to avoid high energy intermediates. There are many examples of thermally activated EPT in ground-state reactions and in excited states following photoexcitation and thermal relaxation. Here we report application of ultrafast excitation with absorption and Raman monitoring to detect a photochemically driven EPT process (photo-EPT). In this process, both electrons and protons are transferred during the absorption of a photon. Photo-EPT is induced by intramolecular charge-transfer (ICT) excitation of hydrogen-bonded-base adducts with either a coumarin dye or 4-nitro-4′-biphenylphenol. Femtosecond transient absorption spectral measurements following ICT excitation reveal the appearance of two spectroscopically distinct states having different dynamical signatures. One of these states corresponds to a conventional ICT excited state in which the transferring H+ is initially associated with the proton donor. Proton transfer to the base (B) then occurs on the picosecond time scale. The other state is an ICT-EPT photoproduct. Upon excitation it forms initially in the nuclear configuration of the ground state by application of the Franck–Condon principle. However, due to the change in electronic configuration induced by the transition, excitation is accompanied by proton transfer with the protonated base formed with a highly elongated +H─B bond. Coherent Raman spectroscopy confirms the presence of a vibrational mode corresponding to the protonated base in the optically prepared state

Australian experience of side-to-side isoperistaltic stricturoplasty in Crohn's disease

Background: The Michelassi stricturoplasty has demonstrated efficacy for Crohn's disease in European and American series but has not had uptake in Australia. We report the short-term results of side-to-side isoperistaltic stricturoplasty (SSIS) in an Australian Practice. Methods: Between March 2015 and October 2021 SSIS procedures were performed on Crohn's patients with long segment Crohn's strictures associated with obstructive symptoms, despite best medical therapy. Surgical demographics and results were recorded via inpatient and outpatient follow-up in a prospective database. Results: Twenty-one SSIS performed in 16 patients, nine female, mean age 40 years. Single incision laparoscopic surgery (SILS) was used in 10 patients. The standard Michelassi SSIS used for 11 strictures and a Poggioli variant used for 10. Mean stricture length 32 cm (range 5–100); mean SSIS length 24 cm (range 6–55). Associated bowel resection in seven cases with a mean length of 47 mm. Ten patients had an average of three additional stricturoplasties. Complications included central line sepsis in one, deep surgical site infection in one and superficial wound infection in four patients. Mean duration of operation; 346 min and length of stay 10 days. Conclusion: SSIS techniques are safe for the management of long segment stricturing Crohn's disease. Although not widely used in Australia, surgeons should consider the Michelassi stricturoplasty, and its variants, for long Crohn's strictures as they are isoperistaltic whilst avoiding bowel resection and blind pouches