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1. The dicarbon bonding puzzle viewed with photoelectron imaging

   https://doi.org/10.1038/s41467-019-13039-y  

   Laws, B. A.; Gibson, S. T.; Lewis, B. R.; Field, R. W. (December 2019, Nature Communications)

   null (Ed.)

   Abstract Bonding in the ground state of C $${}_{2}$$ 2 is still a matter of controversy, as reasonable arguments may be made for a dicarbon bond order of $$2$$ 2 , $$3$$ 3 , or $$4$$ 4 . Here we report on photoelectron spectra of the C $${}_{2}^{-}$$ 2 − anion, measured at a range of wavelengths using a high-resolution photoelectron imaging spectrometer, which reveal both the ground $${X}^{1}{\Sigma}_{\mathrm{g}}^{+}$$ X 1 Σ g + and first-excited $${a}^{3}{\Pi}_{{\mathrm{u}}}$$ a 3 Π u electronic states. These measurements yield electron angular anisotropies that identify the character of two orbitals: the diffuse detachment orbital of the anion and the highest occupied molecular orbital of the neutral. This work indicates that electron detachment occurs from predominantly $$s$$ s -like ( $$3{\sigma}_{\mathrm{g}}$$ 3 σ g ) and $$p$$ p -like ( $$1{\pi }_{{\mathrm{u}}}$$ 1 π u ) orbitals, respectively, which is inconsistent with the predictions required for the high bond-order models of strongly $$sp$$ s p -mixed orbitals. This result suggests that the dominant contribution to the dicarbon bonding involves a double-bonded configuration, with 2 $$\pi$$ π bonds and no accompanying $$\sigma$$ σ bond. 

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2. Inclusive quarkonium production in pp collisions at $$\sqrt{s}$$ = 5.02 TeV

   https://doi.org/10.1140/epjc/s10052-022-10896-8  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; et al (January 2023, The European Physical Journal C)

   Abstract This article reports on the inclusive production cross section of several quarkonium states, $$\textrm{J}/\psi $$ J / ψ , $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) , $$\Upsilon \mathrm (1S)$$ Υ ( 1 S ) , $$\Upsilon \mathrm{(2S)}$$ Υ ( 2 S ) , and $$\Upsilon \mathrm{(3S)}$$ Υ ( 3 S ) , measured with the ALICE detector at the LHC, in pp collisions at $$\sqrt{s} = 5.02$$ s = 5.02  TeV. The analysis is performed in the dimuon decay channel at forward rapidity ( $$2.5< y < 4$$ 2.5 < y < 4 ). The integrated cross sections and transverse-momentum ( $$p_{\textrm{T}}$$ p T ) and rapidity ( $$y$$ y ) differential cross sections for $$\textrm{J}/\psi $$ J / ψ , $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) , $$\Upsilon \mathrm (1S)$$ Υ ( 1 S ) , and the $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) -to- $$\textrm{J}/\psi $$ J / ψ cross section ratios are presented. The integrated cross sections, assuming unpolarized quarkonia, are: $$\sigma _{\textrm{J}/\psi }$$ σ J / ψ  ( $$p_{\textrm{T}} <20$$ p T < 20  GeV/c) = 5.88 ± 0.03 ± 0.34 $$ ~\mu $$ μ b, $$\sigma _{\psi \mathrm{(2S)}}$$ σ ψ ( 2 S )  ( $$p_{\textrm{T}} <12$$ p T < 12  GeV/c) = 0.87 ± 0.06 ± 0.10 $$~\mu $$ μ b, $$\sigma _{\Upsilon \mathrm (1S)}$$ σ Υ ( 1 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 45.5 ± 3.9 ± 3.5 nb, $$\sigma _{\Upsilon \mathrm{(2S)}}$$ σ Υ ( 2 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 22.4 ± 3.2 ± 2.7 nb, and $$\sigma _{\Upsilon \mathrm{(3S)}}$$ σ Υ ( 3 S )  ( $$p_{\textrm{T}} <15$$ p T < 15  GeV/c) = 4.9 ± 2.2 ± 1.0 nb, where the first (second) uncertainty is the statistical (systematic) one. For the first time, the cross sections of the three $$\Upsilon $$ Υ states, as well as the $$\psi \mathrm{(2S)}$$ ψ ( 2 S ) one as a function of $$p_{\textrm{T}}$$ p T and $$y$$ y , are measured at $$\sqrt{s} = 5.02$$ s = 5.02  TeV at forward rapidity. These measurements also significantly extend the $$\textrm{J}/\psi $$ J / ψ $$p_{\textrm{T}}$$ p T reach and supersede previously published results. A comparison with ALICE measurements in pp collisions at $$\sqrt{s} = 2.76$$ s = 2.76 , 7, 8, and 13 TeV is presented and the energy dependence of quarkonium production cross sections is discussed. Finally, the results are compared with the predictions from several production models. 

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3. Measurement of J/ψ production cross-sections in pp collisions at $$ \sqrt{s} $$ = 5 TeV

   https://doi.org/10.1007/JHEP11(2021)181  

   Aaij, R.; Abdelmotteleb, A. S.; Abellán Beteta, C.; Ackernley, T.; Adeva, B.; Adinolfi, M.; Afsharnia, H.; Agapopoulou, C.; Aidala, C. A.; Aiola, S.; et al (November 2021, Journal of High Energy Physics)

   A bstract The production cross-sections of J/ψ mesons in proton-proton collisions at a centre-of-mass energy of $$ \sqrt{s} $$ s = 5 TeV are measured using a data sample corresponding to an integrated luminosity of 9 . 13 ± 0 . 18 pb − 1 , collected by the LHCb experiment. The cross-sections are measured differentially as a function of transverse momentum, p T , and rapidity, y , and separately for J/ψ mesons produced promptly and from beauty hadron decays (nonprompt). With the assumption of unpolarised J/ψ mesons, the production cross-sections integrated over the kinematic range 0 < p T < 20 GeV/ c and 2 . 0 < y < 4 . 5 are $$ {\displaystyle \begin{array}{c}{\sigma}_{\mathrm{prompt}}\ J/\psi =8.154\pm 0.010\pm 0.283\ \upmu \mathrm{b},\\ {}{\sigma}_{\mathrm{nonprompt}}\ J/\psi =0.820\pm 0.003\pm 0.034\ \upmu \mathrm{b},\end{array}} $$ σ prompt J / ψ = 8.154 ± 0.010 ± 0.283 μb , σ nonprompt J / ψ = 0.820 ± 0.003 ± 0.034 μb , where the first uncertainties are statistical and the second systematic. These cross-sections are compared with those at $$ \sqrt{s} $$ s = 8 TeV and 13 TeV, and are used to update the measurement of the nuclear modification factor in proton-lead collisions for J/ψ mesons at a centre-of-mass energy per nucleon pair of $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5 TeV. The results are compared with theoretical predictions. 

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4. Random Interpolating Sequences in the Polydisc and the Unit Ball

   https://doi.org/10.1007/s40315-022-00448-2  

   Dayan, Alberto; Wick, Brett D.; Wu, Shengkun (March 2023, Computational Methods and Function Theory)

   Abstract We study almost surely separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0–1 Komolgorov law for a sequence to be interpolating almost surely for all the Besov–Sobolev spaces $$B_{2}^{\sigma }\left( \mathbb {B}_{d}\right) $$ B 2 σ B d , in the range $$0 < \sigma \le 1 / 2$$ 0 < σ ≤ 1 / 2 . For those spaces, such interpolating sequences coincide with interpolating sequences for their multiplier algebras, thanks to the Pick property. This is not the case for the Hardy space $$\mathrm {H}^2(\mathbb {D}^d)$$ H 2 ( D d ) and its multiplier algebra $$\mathrm {H}^\infty (\mathbb {D}^d)$$ H ∞ ( D d ) : in the polydisc, we obtain a sufficient and a necessary condition for a sequence to be $$\mathrm {H}^\infty (\mathbb {D}^d)$$ H ∞ ( D d ) -interpolating almost surely. Those two conditions do not coincide, due to the fact that the deterministic starting point is less descriptive of interpolating sequences than its counterpart for the unit ball. On the other hand, we give the $$0-1$$ 0 - 1 law for random interpolating sequences for $$\mathrm {H}^2(\mathbb {D}^d)$$ H 2 ( D d ) . 

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5. Stable isoperimetric ratios and the Hodge Laplacian of hyperbolic manifolds

   https://doi.org/10.1112/topo.12291  

   Rudd, Cameron Gates (May 2023, Journal of Topology)

   Abstract We show that for a closed hyperbolic 3‐manifold, the size of the first eigenvalue of the Hodge Laplacian acting on coexact 1‐forms is comparable to an isoperimetric ratio relating geodesic length and stable commutator length with comparison constants that depend polynomially on the volume and on a lower bound on injectivity radius, refining estimates of Lipnowski and Stern. We use this estimate to show that there exist sequences of closed hyperbolic 3‐manifolds with injectivity radius bounded below and volume going to infinity for which the 1‐form Laplacian has spectral gap vanishing exponentially fast in the volume. 

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