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1. Quadrupolar charge dynamics in the nonmagnetic FeSe _1−x S _x superconductors

   https://doi.org/10.1073/pnas.2020585118  

   Zhang, Weilu; Wu, Shangfei; Kasahara, Shigeru; Shibauchi, Takasada; Matsuda, Yuji; Blumberg, Girsh (May 2021, Proceedings of the National Academy of Sciences)

   null (Ed.)

   We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic F e S e 1 − x S x superconductor. We observe two types of long-wavelength X Y symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at T S ( x ) , a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the X Y symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward T S ( x ) . The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration x c r ≈ 0.16 , while the pseudogap size decreases with the suppression of T S ( x ) . We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed. 

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2. Multiplicity dependence of $$\pi $$, K, and p production in pp collisions at $$\sqrt{s} = 13$$ TeV

   https://doi.org/10.1140/epjc/s10052-020-8125-1  

   Acharya, S.; Adamová, D.; Adler, A.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; et al (August 2020, The European Physical Journal C)

   null (Ed.)

   Abstract This paper presents the measurements of $$\pi ^{\pm }$$ π ± , $$\mathrm {K}^{\pm }$$ K ± , $$\text {p}$$ p and $$\overline{\mathrm{p}} $$ p ¯ transverse momentum ( $$p_{\text {T}}$$ p T ) spectra as a function of charged-particle multiplicity density in proton–proton (pp) collisions at $$\sqrt{s}\ =\ 13\ \text {TeV}$$ s = 13 TeV with the ALICE detector at the LHC. Such study allows us to isolate the center-of-mass energy dependence of light-flavour particle production. The measurements reported here cover a $$p_{\text {T}}$$ p T range from 0.1 to 20 $$\text {GeV}/c$$ GeV / c and are done in the rapidity interval $$|y|<0.5$$ | y | < 0.5 . The $$p_{\text {T}}$$ p T -differential particle ratios exhibit an evolution with multiplicity, similar to that observed in pp collisions at $$\sqrt{s}\ =\ 7\ \text {TeV}$$ s = 7 TeV , which is qualitatively described by some of the hydrodynamical and pQCD-inspired models discussed in this paper. Furthermore, the $$p_{\text {T}}$$ p T -integrated hadron-to-pion yield ratios measured in pp collisions at two different center-of-mass energies are consistent when compared at similar multiplicities. This also extends to strange and multi-strange hadrons, suggesting that, at LHC energies, particle hadrochemistry scales with particle multiplicity the same way under different collision energies and colliding systems. 

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3. Short Proof of the Asymptotic Confirmation of the Faudree-Lehel Conjecture

   https://doi.org/10.37236/11413  

   Przybyło, Jakub; Wei, Fan (October 2023, The Electronic Journal of Combinatorics)

   Given a simple graph $$G$$, the irregularity strength of $$G$$, denoted $s(G)$, is the least positive integer $$k$$ such that there is a weight assignment on edges $$f: E(G) \to \{1,2,\dots, k\}$$ for which each vertex weight $$f^V(v):= \sum_{u: \{u,v\}\in E(G)} f(\{u,v\})$$ is unique amongst all $$v\in V(G)$$. In 1987, Faudree and Lehel conjectured that there is a constant $$c$$ such that $$s(G) \leq n/d + c$$ for all $$d$$-regular graphs $$G$$ on $$n$$ vertices with $d>1$, whereas it is trivial that $$s(G) \geq n/d$$. In this short note we prove that the Faudree-Lehel Conjecture holds when $$d \geq n^{0.8+\epsilon}$$ for any fixed $$\epsilon >0$$, with a small additive constant $c=28$ for $$n$$ large enough. Furthermore, we confirm the conjecture asymptotically by proving that for any fixed $$\beta\in(0,1/4)$$ there is a constant $$C$$ such that for all $$d$$-regular graphs $$G$$, $$s(G) \leq \frac{n}{d}(1+\frac{C}{d^{\beta}})+28$$, extending and improving a recent result of Przybyło that $$s(G) \leq \frac{n}{d}(1+ \frac{1}{\ln^{\epsilon/19}n})$$ whenever $$d\in [\ln^{1+\epsilon} n, n/\ln^{\epsilon}n]$$ and $$n$$ is large enough. 

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4. Measurement of ψ (2S) production as a function of charged-particle pseudorapidity density in pp collisions at $$ \sqrt{s} $$ = 13 TeV and p–Pb collisions at $$ \sqrt{s_{\textrm{NN}}} $$ = 8.16 TeV with ALICE at the LHC

   https://doi.org/10.1007/JHEP06(2023)147  

   Acharya, S.; Adamová, D.; Adler, A.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, S.; Ahn, S. U.; Ahuja, I.; et al (June 2023, Journal of High Energy Physics)

   A bstract Production of inclusive charmonia in pp collisions at center-of-mass energy of $$ \sqrt{s} $$ s = 13 TeV and p–Pb collisions at center-of-mass energy per nucleon pair of $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 8 . 16 TeV is studied as a function of charged-particle pseudorapidity density with ALICE. Ground and excited charmonium states ( J/ψ , ψ (2S)) are measured from their dimuon decays in the interval of rapidity in the center-of-mass frame 2 . 5 < y cms < 4 . 0 for pp collisions, and 2 . 03 < y cms < 3 . 53 and −4 . 46 < y cms < −2 . 96 for p–Pb collisions. The charged-particle pseudorapidity density is measured around midrapidity (| η | < 1 . 0). In pp collisions, the measured charged-particle multiplicity extends to about six times the average value, while in p-Pb collisions at forward (backward) rapidity a multiplicity corresponding to about three (four) times the average is reached. The ψ (2S) yield increases with the charged-particle pseudorapidity density. The ratio of ψ (2S) over J/ψ yield does not show a significant multiplicity dependence in either colliding system, suggesting a similar behavior of J/ψ and ψ (2S) yields with respect to charged-particle pseudorapidity density. Results for the ψ (2S) yield and its ratio with respect to J/ψ agree with available model calculations. 

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5. Forbidding $$K_{2,t}$$ Traces in Triple Systems

   https://doi.org/10.37236/9760  

   Luo, Ruth; Spiro, Sam (April 2021, The Electronic Journal of Combinatorics)

   Let $$H$$ and $$F$$ be hypergraphs. We say $$H$$ {\em contains $$F$$ as a trace} if there exists some set $$S \subseteq V(H)$$ such that $$H|_S:=\{E\cap S: E \in E(H)\}$$ contains a subhypergraph isomorphic to $$F$$. In this paper we give an upper bound on the number of edges in a $$3$$-uniform hypergraph that does not contain $$K_{2,t}$$ as a trace when $$t$$ is large. In particular, we show that $$\lim_{t\to \infty}\lim_{n\to \infty} \frac{\mathrm{ex}(n, \mathrm{Tr}_3(K_{2,t}))}{t^{3/2}n^{3/2}} = \frac{1}{6}.$$ Moreover, we show $$\frac{1}{2} n^{3/2} + o(n^{3/2}) \leqslant \mathrm{ex}(n, \mathrm{Tr}_3(C_4)) \leqslant \frac{5}{6} n^{3/2} + o(n^{3/2})$$. 

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