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1. Partitioned matching games for international kidney exchange

   https://doi.org/10.1007/s10107-025-02200-9  

   Benedek, Márton; Biró, Péter; Kern, Walter; Pálvölgyi, Dömötör; Paulusma, Daniel (February 2025, Mathematical Programming)

   Abstract We introduce partitioned matching games as a suitable model for international kidney exchange programmes, where in each round the total number of available kidney transplants needs to be distributed amongst the participating countries in a “fair” way. A partitioned matching game (N, v) is defined on a graph$$G=(V,E)$$ $G=(V,E)$with an edge weightingwand a partition$$V=V_1 \cup \dots \cup V_n$$ $V=V_1\cup \cdots \cup V_n$. The player set is$$N = \{ 1, \dots , n\}$$ $N=\{1,\cdots ,n\}$, and player$$p \in N$$ $p\in N$owns the vertices in$$V_p$$ $V_p$. The valuev(S) of a coalition $$S \subseteq N$$ $S\subseteq N$is the maximum weight of a matching in the subgraph ofGinduced by the vertices owned by the players in S. If$$|V_p|=1$$ $|V_p|=1$for all$$p\in N$$ $p\in N$, then we obtain the classical matching game. Let$$c=\max \{|V_p| \; |\; 1\le p\le n\}$$ $c=max\left\{\right|V_p\left|\right|1\le p\le n\}$be the width of (N, v). We prove that checking core non-emptiness is polynomial-time solvable if$$c\le 2$$ $c\le 2$but co--hard if$$c\le 3$$ $c\le 3$. We do this via pinpointing a relationship with the known class ofb-matching games and completing the complexity classification on testing core non-emptiness forb-matching games. With respect to our application, we prove a number of complexity results on choosing, out of possibly many optimal solutions, one that leads to a kidney transplant distribution that is as close as possible to some prescribed fair distribution. 

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2. Towards a Schinzel–Wójcik theorem for number fields

   https://doi.org/10.1007/s40879-025-00819-8  

   Pollack, Paul (April 2025, European Journal of Mathematics)

   Abstract Schinzel and Wójcik have shown that for every$$\alpha ,\beta \in \mathbb {Q}^{\times }\hspace{0.55542pt}{\setminus }\hspace{1.111pt}\{\pm 1\}$$ $\alpha ,\beta \in Q^{\times }\backslash \{\pm 1\}$, there are infinitely many primespwhere$$v_p(\alpha )=v_p(\beta )=0$$ $v_p\left(\alpha \right)=v_p\left(\beta \right)=0$and where$$\alpha $$ $\alpha$and$$\beta $$ $\beta$generate the same multiplicative group modp. We prove a weaker result in the same direction for algebraic numbers$$\alpha , \beta $$ $\alpha ,\beta$. Let$$\alpha , \beta \in \overline{\mathbb {Q}} ^{\times }$$ $\alpha ,\beta \in {\overline{Q}}^{\times }$, and suppose$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\alpha )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\alpha \right)|\ne 1$and$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\beta )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\beta \right)|\ne 1$. Then for some positive integer$$C = C(\alpha ,\beta )$$ $C=C(\alpha ,\beta )$, there are infinitely many prime idealsPof Equation missing<#comment/>where$$v_P(\alpha )=v_P(\beta )=0$$ $v_P\left(\alpha \right)=v_P\left(\beta \right)=0$and where the group$$\langle \beta \bmod {P}\rangle $$ $⟨\beta modP⟩$is a subgroup of$$\langle \alpha \bmod {P}\rangle $$ $⟨\alpha modP⟩$with$$[\langle \alpha \bmod {P}\rangle \,{:}\, \langle \beta \bmod {P}\rangle ]$$ $[⟨\alpha modP⟩:⟨\beta modP⟩]$dividingC. A key component of the proof is a theorem of Corvaja and Zannier bounding the greatest common divisor of shiftedS-units. 

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3. 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)

   Abstract 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. 

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4. Multipliers on bi-parameter Haar system Hardy spaces

   https://doi.org/10.1007/s00208-024-02887-9  

   Lechner, R.; Motakis, P.; Müller, P_F_X; Schlumprecht, Th (May 2024, Mathematische Annalen)

   Abstract Let$$(h_I)$$ $\left(h_I\right)$denote the standard Haar system on [0, 1], indexed by$$I\in \mathcal {D}$$ $I\in D$, the set of dyadic intervals and$$h_I\otimes h_J$$ $h_I\otimes h_J$denote the tensor product$$(s,t)\mapsto h_I(s) h_J(t)$$ $(s,t)\mapsto h_I\left(s\right)h_J\left(t\right)$,$$I,J\in \mathcal {D}$$ $I,J\in D$. We consider a class of two-parameter function spaces which are completions of the linear span$$\mathcal {V}(\delta ^2)$$ $V\left({\delta }^2\right)$of$$h_I\otimes h_J$$ $h_I\otimes h_J$,$$I,J\in \mathcal {D}$$ $I,J\in D$. This class contains all the spaces of the formX(Y), whereXandYare either the Lebesgue spaces$$L^p[0,1]$$ $L^p[0,1]$or the Hardy spaces$$H^p[0,1]$$ $H^p[0,1]$,$$1\le p < \infty $$ $1\le p<\infty$. We say that$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$is a Haar multiplier if$$D(h_I\otimes h_J) = d_{I,J} h_I\otimes h_J$$ $D(h_I\otimes h_J)=d_{I,J}{h}_I\otimes h_J$, where$$d_{I,J}\in \mathbb {R}$$ $d_{I,J}\in R$, and ask which more elementary operators factor throughD. A decisive role is played by theCapon projection$$\mathcal {C}:\mathcal {V}(\delta ^2)\rightarrow \mathcal {V}(\delta ^2)$$ $C:V\left({\delta }^2\right)\to V\left({\delta }^2\right)$given by$$\mathcal {C} h_I\otimes h_J = h_I\otimes h_J$$ $C{h}_I\otimes h_J=h_I\otimes h_J$if$$|I|\le |J|$$ $\left|I\right|\le \left|J\right|$, and$$\mathcal {C} h_I\otimes h_J = 0$$ $C{h}_I\otimes h_J=0$if$$|I| > |J|$$ $\left|I\right|>\left|J\right|$, as our main result highlights: Given any bounded Haar multiplier$$D:X(Y)\rightarrow X(Y)$$ $D:X\left(Y\right)\to X\left(Y\right)$, there exist$$\lambda ,\mu \in \mathbb {R}$$ $\lambda ,\mu \in R$such that$$\begin{aligned} \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C})\text { approximately 1-projectionally factors through }D, \end{aligned}$$ $\begin{array}{c}\lambda C+\mu (\text{Id}-C)\text{approximately 1-projectionally factors through}D,\end{array}$i.e., for all$$\eta > 0$$ $\eta >0$, there exist bounded operatorsA, Bso thatABis the identity operator$${{\,\textrm{Id}\,}}$$ $\text{Id}$,$$\Vert A\Vert \cdot \Vert B\Vert = 1$$ $\Vert A\Vert ·\Vert B\Vert =1$and$$\Vert \lambda \mathcal {C} + \mu ({{\,\textrm{Id}\,}}-\mathcal {C}) - ADB\Vert < \eta $$ $\Vert \lambda C+\mu (\text{Id}-C)-ADB\Vert <\eta$. Additionally, if$$\mathcal {C}$$ $C$is unbounded onX(Y), then$$\lambda = \mu $$ $\lambda =\mu$and then$${{\,\textrm{Id}\,}}$$ $\text{Id}$either factors throughDor$${{\,\textrm{Id}\,}}-D$$ $\text{Id}-D$. 

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5. QLBT: a linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles

   https://doi.org/10.1140/epjc/s10052-022-10308-x  

   Liu, Feng-Lei; Xing, Wen-Jing; Wu, Xiang-Yu; Qin, Guang-You; Cao, Shanshan; Wang, Xin-Nian (April 2022, The European Physical Journal C)

   Abstract We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor$$R_\mathrm {AA}$$ $R_{\mathrm{AA}}$and the elliptic flow$$v_2$$ $v_2$ofDmesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on theDmeson$$R_\mathrm {AA}$$ $R_{\mathrm{AA}}$and$$v_2$$ $v_2$, we extract the heavy quark transport parameter$$\hat{q}$$ $\hat{q}$and diffusion coefficient$$D_\mathrm {s}$$ $D_s$in the temperature range of$$1-4~T_\mathrm {c}$$ $1-4T_c$, and compare them with the lattice QCD results and other phenomenological studies. 

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