Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Pleba\'nski

We present first heavenly equation of Pleba\'nski in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse Noether theorem in the Hamiltonian form, obtain all the integrals of motion corresponding to each variational (Noether) symmetry. We derive two linearly independent recursion operators for symmetries of this system related by a discrete symmetry of both the two-component system and its symmetry condition. Acting by these operators on the first Hamiltonian operator $J_0$ we obtain second and third Hamiltonian operators. However, we were not able to find Hamiltonian densities corresponding to the latter two operators. Therefore, we construct two recursion operators, which are either even or odd, respectively, under the above-mentioned discrete symmetry. Acting with them on $J_0$, we generate another two Hamiltonian operators $J_+$ and $J_-$ and find the corresponding Hamiltonian densities, thus obtaining second and third Hamiltonian representations for the first heavenly equation in a two-component form. Using P. Olver's theory of the functional multi-vectors, we check that the linear combination of $J_0$, $J_+$ and $J_-$ with arbitrary constant coefficients satisfies Jacobi identities. Since their skew symmetry is obvious, these three operators are compatible Hamiltonian operators and hence we obtain a tri-Hamiltonian representation of the first heavenly equation. Our well-founded conjecture applied here is that P. Olver's method works fine for nonlocal operators and our proof of the Jacobi identities and bi-Hamiltonian structures crucially depends on the validity of this conjecture.Comment: Some text overlap with our paper arXiv:1510.03666 is caused by our use here of basically the same method for discovering the Hamiltonian and bi-Hamiltonian structures of the equation, but the equation considered here and the results are totally different from arXiv:1510.0366

Multi-aspect analysis of ureteral access sheath usage in retrograde intrarenal surgery: A RIRSearch group study

Objective: To evaluate the effect of ureteral access sheath (UAS) use and calibration change on stone-free rate and complications of retrograde intrarenal surgery (RIRS). Methods: Data from 568 patients undergoing RIRS for kidney or upper ureteral stones were retrospectively included. Firstly, patients were compared after 1:1 propensity score matching, according to UAS usage during RIRS (UAS used [+] 87 and UAS non-used [?] 87 patients). Then all UAS+ patients (n=481) were subdivided according to UAS calibration: 9.5–11.5 Fr, 10–12 Fr, 11–13 Fr, and 13–15 Fr. Primary outcomes of the study were the success and complications of RIRS. Results: Stone-free rate of UAS+ patients (86.2%) was significantly higher than UAS? patients (70.1%) after propensity score matching (p=0.01). Stone-free rate increased with higher caliber UAS (9.5–11.5 Fr: 66.7%; 10–12 Fr: 87.3%; 11–13 Fr: 91.3%; 13–15 Fr: 100%; p<0.0001). Postoperative complications of UAS+ patients (11.5%) were significantly lower than UAS? patients (27.6%) (p=0.01). Complications (8.7%) with 9.5–11.5 Fr UAS was lower than thicker UAS (17.3%) but was not statistically significant (p=0.08). UAS usage was an independent factor predicting stone-free status or peri- and post-operative complications (odds ratio [OR] 3.654, 95% confidence interval [CI] 1.314–10.162; OR 4.443, 95% CI 1.350–14.552; OR 4.107, 95% CI 1.366–12.344, respectively). Conclusion: Use of UAS in RIRS may increase stone-free rates, which also increase with higher caliber UAS. UAS usage may reduce complications; however, complications seemingly increase with higher UAS calibration. © 2022 Editorial Office of Asian Journal of Urolog

A variational approach to waveform design for synthetic aperture imaging

Abstract. We derive an optimal transmit waveform for filtered backprojectionbased synthetic-aperture imaging. The waveform is optimal in terms of minimising the mean square error (MSE) in the resulting image. Our optimization is performed in two steps: First, we consider the minimum-mean-square-error (MMSE) for an arbitrary but fixed waveform, and derive the corresponding filter for the filtered backprojection reconstruction. Second, the MMSE is further reduced by finding an optimal transmit waveform. The transmit waveform is derived for stochastic models of the scattering objects of interest (targets), other scattering objects (clutter), and additive noise. We express the waveform in terms of spatial spectra for the random fields associated with target and clutter, and the spectrum for the noise process. This approach results in a constraint that involves only the amplitude of the Fourier transform of the transmit waveform. Therefore, considerable flexibility is left for incorporating additional requirements, such as minimal variation of transmit amplitude and phase-coding

4,5-Bis(2,4-di-tert-butyl­phen­oxy)phthalonitrile

In the title compound, C36H44N2O2, the dihedral angles between the phthalonitrile ring and the two di-tert-butyl­benzene rings are 68.134 (8) and 70.637 (11)°. The two nitrile groups are almost coplanar with the phthalonitrile ring except for one of the N atoms which deviates from the plane by 0.125 (4) Å. One of the tert-butyl groups is disordered over two orientations, with refined occupancies of 0.814 (6) and 0.186 (6). Intra­molecular C—H⋯O inter­actions stabilize the molecular structure. The crystal packing is stabilized by inter­molecular C—H⋯N inter­actions

Mating type idiomorphs of Pyrenophora teres in Turkey

Pyrenophora teres f. maculata (Ptm) and Pyrenophora teres f. teres (Ptt) causes spot form and net form of net blotch diseases of barley, respectively. Although both forms of P. teres are morphologically similar, their symptoms and genetic background differ. In this study, 175 single spore (109 Ptm and 66 Ptt) isolates obtained from different regions of Turkey were evaluated for their mating type distribution and prevalence. Fungal isolates of both forms were verified using species-speci.c polymerase chain reaction (PCR) primers. For mating type determination studies, duplex PCR was performed using MAT-specific single nucleotide polymorphism primers. Sixty and 49 of 109 Ptm isolates were found as MAT1-1 and MAT1-2 types, respectively and 43 and 23 of 66 Ptt isolates were found as MAT1-1 and MAT1-2 types, respectively. These results show the possibility of sexual reproduction among the Ptm isolates in Turkey and Ptt population of Central Anatolia, Turkey. However, the overall pattern of Ptt isolates did not support the sexual reproduction hypothesis in Turkey. Sexual reproduction in the life cycle of P. teres is important since it could lead to genetic and pathogenic variation. As a result of new sexual combinations more virulent pathotypes of P. teres may occur