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1. Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings

   https://doi.org/10.1017/fms.2020.60  

   Chirvasitu, Alex; Kanda, Ryo; Smith, S. Paul (January 2021, Forum of Mathematics, Sigma)

   null (Ed.)

   Abstract The elliptic algebras in the title are connected graded $$\mathbb {C}$$ -algebras, denoted $$Q_{n,k}(E,\tau )$$ , depending on a pair of relatively prime integers $$n>k\ge 1$$ , an elliptic curve E and a point $$\tau \in E$$ . This paper examines a canonical homomorphism from $$Q_{n,k}(E,\tau )$$ to the twisted homogeneous coordinate ring $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ on the characteristic variety $$X_{n/k}$$ for $$Q_{n,k}(E,\tau )$$ . When $$X_{n/k}$$ is isomorphic to $E^g$ or the symmetric power $S^gE$ , we show that the homomorphism $$Q_{n,k}(E,\tau ) \to B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ is surjective, the relations for $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ are generated in degrees $$\le 3$$ and the noncommutative scheme $$\mathrm {Proj}_{nc}(Q_{n,k}(E,\tau ))$$ has a closed subvariety that is isomorphic to $E^g$ or $S^gE$ , respectively. When $$X_{n/k}=E^g$$ and $$\tau =0$$ , the results about $$B(X_{n/k},\sigma ',\mathcal {L}^{\prime }_{n/k})$$ show that the morphism $$\Phi _{|\mathcal {L}_{n/k}|}:E^g \to \mathbb {P}^{n-1}$$ embeds $E^g$ as a projectively normal subvariety that is a scheme-theoretic intersection of quadric and cubic hypersurfaces. 

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2. Search for the lepton-flavour violating decays B0 → K*0τ±μ∓

   https://doi.org/10.1007/JHEP06(2023)143  

   Aaij, R.; Abdelmotteleb, A. S.; Abellan Beteta, C.; Abudinén, F.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Agapopoulou, C.; Aidala, C. A.; et al (June 2023, Journal of High Energy Physics)

   A bstract A first search for the lepton-flavour violating decays B 0 → K *0 τ ± μ ∓ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb − 1 . No significant signal is observed, and upper limits on the branching fractions are determined to be $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{+}{\mu}^{-}\right)<1.0(1.2)\times {10}^{-5} $$ B B 0 → K ∗ 0 τ + μ − < 1.0 1.2 × 10 − 5 and $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{-}{\mu}^{+}\right)<8.2(9.8)\times {10}^{-6} $$ B B 0 → K ∗ 0 τ − μ + < 8.2 9.8 × 10 − 6 at the 90% (95%) confidence level. 

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3. Effect of gas viscosity on the interfacial instability development in a two-phase mixing layer

   https://doi.org/10.1016/j.ijmultiphaseflow.2024.105026  

   Azad, Tanjina; Ling, Yue (December 2024, International Journal of Multiphase Flow)

   The interfacial instability in a two-phase mixing layers between parallel gas and liquid streams is important to two-phase atomization. Depending on the inflow conditions and fluid properties, interfacial instability can be convective or absolute. The goal of the present study is to investigate the impact of gas viscosity on the interfacial instability. Both interface-resolved simulations and linear stability analysis (LSA) have been conducted. In LSA, the Orr–Sommerfeld equation is solved to analyze the spatio-temporal viscous modes. When the gas viscosity decreases, the Reynold number (Re) increases accordingly. The LSA demonstrates that when Re is higher than a critical threshold, the instability transitions from the absolute to the convective (A/C) regimes. Such a Re-induced A/C transition is also observed in the numerical simulations, though the critical Re observed in simulations is significantly lower than that predicted by LSA. The LSA results indicate that the temporal growth rate decreases with Re. When the growth rate reaches zero, the A/C transition will occur. The Re-induced A/C transition is observed in both confined and unconfined mixing layers and also in cases with low and high gas-to-liquid density ratios. In the transition from typical absolute and convective regimes, a weak absolute regime is identified in the simulations, for which the spectrograms show both the absolute and convective modes. The dominant frequency in the weak absolute regime can be influenced by the perturbation introduced at the inlet. The simulation results also show that the wave propagation speed can vary in space. In the absolute instability regime, the wave propagation speed agrees well with the absolute mode celerity near the inlet and increases to the Dimotakis speed further downstream. 

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4. Evidence for the singly Cabibbo-suppressed decay $$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$ and search for $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ and Ω−K+ decays at Belle

   https://doi.org/10.1007/JHEP01(2023)055  

   Han, X.; Jia, S.; Yuan, L.; Shen, C. P.; Adachi, I.; Ahn, J. K.; Aihara, H.; Asner, D. M.; Aushev, T.; Ayad, R.; et al (January 2023, Journal of High Energy Physics)

   A bstract Using a data sample of 980 fb − 1 collected with the Belle detector at the KEKB asymmetric-energy e + e − collider, we study for the first time the singly Cabibbo-suppressed decays $$ {\Omega}_c^0\to {\Xi}^{-}{\pi}^{+} $$ Ω c 0 → Ξ − π + and Ω − K + and the doubly Cabibbo-suppressed decay $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ Ω c 0 → Ξ − K + . Evidence for an $$ {\Omega}_c^0 $$ Ω c 0 signal in the $$ {\Omega}_c^0 $$ Ω c 0 → Ξ − π + mode is reported with a significance of 4 . 5 σ including systematic uncertainties. The ratio of branching fractions to the normalization mode $$ {\Omega}_c^0 $$ Ω c 0 → Ω − π + is measured to be $$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{\pi}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)=0.253\pm 0.052\left(\textrm{stat}.\right)\pm 0.030\left(\textrm{syst}.\right). $$ B Ω c 0 → Ξ − π + / B Ω c 0 → Ω − π + = 0.253 ± 0.052 stat . ± 0.030 syst . . No significant signals of $$ {\Omega}_c^0\to {\Xi}^{-}{K}^{+} $$ Ω c 0 → Ξ − K + and Ω − K + modes are found. The upper limits at 90% confidence level on ratios of branching fractions are determined to be $$ \mathcal{B}\left({\Omega}_c^0\to {\Xi}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.070 $$ B Ω c 0 → Ξ − K + / B Ω c 0 → Ω − π + < 0.070 and $$ \mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{K}^{+}\right)/\mathcal{B}\left({\Omega}_c^0\to {\Omega}^{-}{\pi}^{+}\right)<0.29. $$ B Ω c 0 → Ω − K + / B Ω c 0 → Ω − π + < 0.29 . 

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5. Measurement of pressure gradients near the interface in the viscous fingering instability

   https://doi.org/10.1103/PhysRevFluids.9.053902  

   Gowen, Savannah D; Videbæk, Thomas E; Nagel, Sidney R (May 2024, Physical Review Fluids)

   The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth. Published by the American Physical Society2024 

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