More Like this

1. The immersion poset on partitions

   https://doi.org/10.1007/s10801-025-01380-z  

   Johnston, Lisa ; Kenepp, David ; Nguyen, Evuilynn ; Paul, Digjoy ; Schilling, Anne ; Simone, Mary_Claire ; Zhou, Regina ( February 2025 , Journal of Algebraic Combinatorics)

   We introduce the immersion poset$$({\mathcal {P}}(n), \leqslant _I)$$$(P\left(n\right),{⩽}_I)$on partitions, defined by$$\lambda \leqslant _I \mu $$$\lambda {⩽}_I\mu$if and only if$$s_\mu (x_1, \ldots , x_N) - s_\lambda (x_1, \ldots , x_N)$$$s_{\mu }(x_1,\dots ,x_N)-s_{\lambda }(x_1,\dots ,x_N)$is monomial-positive. Relations in the immersion poset determine when irreducible polynomial representations of$$GL_N({\mathbb {C}})$$$G{L}_N\left(C\right)$form an immersion pair, as defined by Prasad and Raghunathan [7]. We develop injections$$\textsf{SSYT}(\lambda , \nu ) \hookrightarrow \textsf{SSYT}(\mu , \nu )$$$\mathrm{SSYT}(\lambda ,\nu )\hookrightarrow \mathrm{SSYT}(\mu ,\nu )$on semistandard Young tableaux given constraints on the shape of$$\lambda $$$\lambda$, and present results on immersion relations among hook and two column partitions. The standard immersion poset$$({\mathcal {P}}(n), \leqslant _{std})$$$(P\left(n\right),{⩽}_{\mathrm{std}})$is a refinement of the immersion poset, defined by$$\lambda \leqslant _{std} \mu $$$\lambda {⩽}_{\mathrm{std}}\mu$if and only if$$\lambda \leqslant _D \mu $$$\lambda {⩽}_D\mu$in dominance order and$$f^\lambda \leqslant f^\mu $$$f^{\lambda }⩽f^{\mu }$, where$$f^\nu $$$f^{\nu }$is the number of standard Young tableaux of shape$$\nu $$$\nu$. We classify maximal elements of certain shapes in the standard immersion poset using the hook length formula. Finally, we prove Schur-positivity of power sum symmetric functions on conjectured lower intervals in the immersion poset, addressing questions posed by Sundaram [12].

    

   more » « less
2. Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations

   https://doi.org/10.1007/s00526-025-02929-3  

   Dong, Hongjie ; Kitano, Shuhei ( February 2025 , Calculus of Variations and Partial Differential Equations)

   We obtain new$$L_p$$$L_p$estimates for subsolutions to fully nonlinear equations. Based on our$$L_p$$$L_p$estimates, we further study several topics such as the third and fourth order derivative estimates for concave fully nonlinear equations, critical exponents of$$L_p$$$L_p$estimates and maximum principles, and the existence and uniqueness of solutions to fully nonlinear equations on the torus with free terms in the$$L_p$$$L_p$spaces or in the space of Radon measures.

    

   more » « less
3. Black hole in discrete gravity

   https://doi.org/10.1140/epjc/s10052-024-12648-2  

   Chamseddine, Ali H. ; Malaeb, Ola ; Najem, Sara ( March 2024 , The European Physical Journal C)

   We study the metric corresponding to a three-dimensional coset spaceSO(4)/SO(3) in the lattice setting. With the use of three integers$$n_1, n_2$$$n_1,n_2$, and$$n_3$$$n_3$, and a length scale,$$l_{\mu }$$$l_{\mu }$, the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied.

    

   more » « less
4. Spin density matrix elements in exclusive $$\rho ^0$$ meson muoproduction

   https://doi.org/10.1140/epjc/s10052-023-11359-4  

   Alexeev, G D ; Alexeev, M G ; Alice, C ; Amoroso, A ; Andrieux, V ; Anosov, V ; Augsten, K ; Augustyniak, W ; Azevedo, C_D R ; Badelek, B ; et al ( October 2023 , The European Physical Journal C)

   We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$${\mu }^{+}$and$$ \mu ^{-}$$${\mu }^{-}$beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/$$c^2$$$c^2$$$< W<$$$<W<$17.0 GeV/$$c^2$$$c^2$, 1.0 (GeV/c)$$^2$$${}^2$$$< Q^2<$$$<Q^2<$10.0 (GeV/c)$$^2$$${}^2$and 0.01 (GeV/c)$$^2$$${}^2$$$< p_{\textrm{T}}^2<$$$<p_{\text{T}}^2<$0.5 (GeV/c)$$^2$$${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$$Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$$p_{\text{T}}$the transverse momentum of the$$\rho ^0$$${\rho }^0$meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($$\gamma ^*_T \rightarrow V^{ }_L$$${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive$$\rho ^0$$${\rho }^0$production.

    

   more » « less
5. $$^{222}$$Rn  emanation measurements for the XENON1T experiment

   https://doi.org/10.1140/epjc/s10052-020-08777-z  

   XENON Collaboration ; Aprile, E. ; Aalbers, J. ; Agostini, F. ; Alfonsi, M. ; Althueser, L. ; Amaro, F. D. ; Antochi, V. C. ; Angelino, E. ; Angevaare, J. R. ; et al ( April 2021 , The European Physical Journal C)

   The selection of low-radioactive construction materials is of utmost importance for the success of low-energy rare event search experiments. Besides radioactive contaminants in the bulk, the emanation of radioactive radon atoms from material surfaces attains increasing relevance in the effort to further reduce the background of such experiments. In this work, we present the$$^{222}$$${}^{222}$Rn emanation measurements performed for the XENON1T dark matter experiment. Together with the bulk impurity screening campaign, the results enabled us to select the radio-purest construction materials, targeting a$$^{222}$$${}^{222}$Rn activity concentration of$$10\,\mathrm{\,}\upmu \mathrm{Bq}/\mathrm{kg}$$$10\mu \mathrm{Bq}/\mathrm{kg}$in$$3.2\,\mathrm{t}$$$3.2t$of xenon. The knowledge of the distribution of the$$^{222}$$${}^{222}$Rn sources allowed us to selectively eliminate problematic components in the course of the experiment. The predictions from the emanation measurements were compared to data of the$$^{222}$$${}^{222}$Rn activity concentration in XENON1T. The final$$^{222}$$${}^{222}$Rn activity concentration of$$(4.5\pm 0.1)\,\mathrm{\,}\upmu \mathrm{Bq}/\mathrm{kg}$$$(4.5\pm 0.1)\mu \mathrm{Bq}/\mathrm{kg}$in the target of XENON1T is the lowest ever achieved in a xenon dark matter experiment.

    

   more » « less