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The spontaneous conversion of muonium to antimuonium is one of the interesting charged lepton flavor violation phenomena, offering a sensitive probe of potential new physics and serving as a tool to constrain the parameter space beyond the Standard Model. Utilizing a high-intensity muon beam, a Michel electron magnetic spectrometer and a positron transport solenoid together with a positron detection system, MACE aims to discover or constrain this rare process at the conversion probability beyond the level of $10^{-13}$. This report provides an overview of the theoretical framework and detailed experimental design in the search for the muonium-to-antimuonium conversion., Comment: 115 pages, 59 figures

We construct a unique global solution to the Cauchy problem of the 3D Boltzmann equation for initial data around the Maxwellian in the spatially critical homogeneous Besov space $\widetilde{L}^2_{\xi}(\dot{B}_{2,1}^{1/2}\cap\dot{B}_{2,1}^{3/2})$. In addition, under the condition that the low-frequency part of initial perturbation is bounded in $\widetilde{L}^2_{\xi}(\dot{B}_{2,\infty}^{\sigma_{0}})$ with $-3/2\leq\sigma_{0}<1/2$, it is shown that the solution converges to its equilibrium in large times with the optimal rate of $\mathcal{O}(t^{-(\sigma-\sigma_{0})/2})$ in $\widetilde{L}^2_{\xi}(\dot{B}_{2,1}^{\sigma})$ with some $\sigma>\sigma_0$, and the microscopic part decays at an enhanced rate of $\mathcal{O}(t^{-(\sigma-\sigma_{0})/2-1/2})$. In contrast to [19], the usual $L^2$ estimates are not necessary in our approach, which provides a new understanding of hypocoercivity theory for the Boltzmann equation allowing to construct the Lyapunov functional with different dissipation rates at low and high frequencies. Furthermore, a time-weighted Lyapunov energy argument can be developed to deduce the optimal time-decay estimates., Comment: 35 pages

We consider the chemotaxis-Navier-Stokes system with generalized fluid dissipation in $\mathbb{R}^3$: \begin{eqnarray*} \begin{cases} \partial_t n+u\cdot \nabla n=\Delta n- \nabla \cdot (\chi(c)n \nabla c),\\ \partial_t c+u \cdot \nabla c=\Delta c-nf(c),\\ \partial_t u +u \cdot \nabla u+\nabla P=-(-\Delta)^\alpha u-n\nabla \phi,\\ \nabla \cdot u=0, \end{cases} \end{eqnarray*} which describes the motion of swimming bacteria or bacillus subtilis suspended to water flows. First, we prove some blow-up criteria of strong solutions to the Cauchy problem, including the Prodi-Serrin type criterion ($\alpha>\frac{3}{4}$) and the Beir${\rm\tilde{a}}$o da Veiga type criterion $(\alpha>\frac{1}{2})$. Then, we verify the global existence and uniqueness of strong solutions for arbitrarily large initial fluid velocity and bacteria density for $\alpha\geq \frac{5}{4}$. Furthermore, in the scenario of $\frac{3}{4}<\alpha<\frac{5}{4}$, we establish uniform regularity estimates and optimal time-decay rates of global solutions if the $L^2$-norm of initial data is small. To our knowledge, this is the first result concerning the global existence and large-time behavior of strong solutions for the chemotaxis-Navier-Stokes equations with possibly large oscillations., Comment: 39 pages

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness of classical solutions being a sharp small perturbation of constant equilibrium in a critical regularity setting, uniformly with respect to the relaxation parameter $\varepsilon>0$. Then, for all times $t>0$, we derive quantitative error estimates at the rate $O(\varepsilon)$ between the rescaled Euler-Maxwell system and the limit drift-diffusion model. To the best of our knowledge, this work provides the first global-in-time strong convergence for the relaxation procedure in the case of ill-prepared data. In order to prove our results, we develop a new characterization of the dissipation structure for the linearized Euler-Maxwell system with respect to the relaxation parameter $\varepsilon$. This is done by partitioning the frequency space into three distinct regimes: low, medium and high frequencies, each associated with a different behaviour of the solution. Then, in each regime, the use of efficient unknowns and Lyapunov functionals based on the hypocoercivity theory leads to uniform a priori estimates., Comment: 32pages

We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in $\mathbb{R}^{d}$ ($d\geq1$), where the interaction force is given by $\nabla(-\Delta)^{\smash{\frac{\alpha-d}{2}}}(\rho-\bar{\rho})$ with $d-2<\alpha

The emerging research shows that lncRNAs are associated with a series of complex human diseases. However, most of the existing methods have limitations in identifying nonlinear lncRNA-disease associations (LDAs), and it remains a huge challenge to predict new LDAs. Therefore, the accurate identification of LDAs is very important for the warning and treatment of diseases. In this work, multiple sources of biomedical data are fully utilized to construct characteristics of lncRNAs and diseases, and linear and nonlinear characteristics are effectively integrated. Furthermore, a novel deep learning model based on graph attention automatic encoder is proposed, called HGATELDA. To begin with, the linear characteristics of lncRNAs and diseases are created by the miRNA-lncRNA interaction matrix and miRNA-disease interaction matrix. Following this, the nonlinear features of diseases and lncRNAs are extracted using a graph attention auto-encoder, which largely retains the critical information and effectively aggregates the neighborhood information of nodes. In the end, LDAs can be predicted by fusing the linear and nonlinear characteristics of diseases and lncRNA. The HGATELDA model achieves an impressive AUC value of 0.9692 when evaluated using a 5-fold cross-validation indicating its superior performance in comparison to several recent prediction models. Meanwhile, the effectiveness of HGATELDA in identifying novel LDAs is further demonstrated by case studies. the HGATELDA model appears to be a viable computational model for predicting LDAs., Comment: 10 pages, 8 figures

The electromagnetic form factors $G_{\rm E}$ and $G_{\rm M}$ of the proton and neutron in the timelike region are extracted in a study of the processes $e^+ e^-\to \bar{p}p$ and $e^+ e^-\to \bar{n}n$. The reaction amplitude is evaluated within the distorted wave Born approximation, with the interaction of the antinucleon-nucleon ($\bar{N}N$) pair taken into account. The latter is constructed within $SU(3)$ chiral effective field theory up to the next-to-leading order. An excellent description of the $e^+ e^-\to \bar{N}N$ data in the energy region from the $\bar{N}N$ threshold up to center-of-mass energies $E_{\rm cm}=2.2$~GeV is achieved. Results for the electromagnetic form factors $G_{\rm E}, G_{\rm M}$, $G_{\rm E}/G_{\rm M}$, and the subtracted effective form factors, $G_{\rm osc}$, are provided. These can be helpful for further studies of the properties of the nucleons., Comment: 37 pages, 10 figures

In this paper, the reaction of electron-positron annihilation into $\Lambda_c^+\bar{\Lambda}_c^-$ is investigated. The $\Lambda_c^+\bar{\Lambda}_c^-$ scattering amplitudes are obtained by solving the Lippmann-Schwinger equation. The contact, annihilation, and two pseudoscalar-exchange potentials are taken into account in the spirit of the chiral effective field theory. The amplitudes of $e^+e^-\to \Lambda_c^+\bar{\Lambda}_c^-$ are constructed by the distorted wave Born approximation method, with the final state interactions of the $\Lambda_c^+\bar{\Lambda}_c^-$ re-scattering implemented. By fitting to the experimental data, the unknown couplings are fixed, and high-quality solutions are obtained. With these amplitudes, the individual electromagnetic form factors in the timelike region, $G_E^{\Lambda_c}$, $G_M^{\Lambda_c}$, and their ratio, $G_E^{\Lambda_c}/G_M^{\Lambda_c}$, are extracted. Both modulus and phases are predicted. These individual electromagnetic form factors reveal new insights into the properties of the $\Lambda_c$. The separated contributions of the Born term, contact, annihilation, as well as the two pseudoscalar exchange potentials to the electromagnetic form factors are isolated. It is found that the Born term dominates the whole energy region. The contact term plays a crucial role in the enhancement near the threshold, and the annihilation term is essential in generating the fluctuation of the electromagnetic form factors., Comment: 9 pages, 7 figures

In this paper, a coherent study of the $e^+e^-$ annihilation into $K^+K^-\pi^0$, $K^0_SK^0_L\pi^0$ and $K^0_SK^\pm\pi^\mp$ is carried out within the framework of resonance chiral theory. The amplitudes are fixed by fitting to the experimental cross-section and invariant mass spectrum. With these amplitudes, one can calculate the hadronic vacuum polarization form factors of these processes. The leading order contributions of $\sigma(e^+e^- \to K\bar{K}\pi)$ to the anomalous magnetic moment of the muon, $(g-2)_\mu$, is obtained as $a_\mu^{\rm HVP,LO}(e^+e^- \to K\bar{K}\pi)=(3.079\pm0.088)\times10^{-10}$ up to $E_{\rm cm}=2.3$ GeV., Comment: 14 pages, 2 figures

Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a compact space, Gr\"ochenig in \cite{G} discussed weighted least squares approximation and least squares quadrature. Inspired by this work, for all $1\le p\le\infty$, we develop weighted least $\ell_p$ approximation induced by a sequence of Marcinkiewicz-Zygmund inequalities in $L_p$ on a compact smooth Riemannian manifold $\Bbb M$ with normalized Riemannian measure (typical examples are the torus and the sphere). In this paper we derive corresponding approximation theorems with the error measured in $L_q,\,1\le q\le\infty$, and least quadrature errors for both Sobolev spaces $H_p^r(\Bbb M), \, r>d/p$ generated by eigenfunctions associated with the Laplace-Beltrami operator and Besov spaces $B_{p,\tau}^r(\Bbb M),\, 0<\tau\le \infty, r>d/p $ defined by best polynomial approximation. Finally, we discuss the optimality of the obtained results by giving sharp estimates of sampling numbers and optimal quadrature errors for the aforementioned spaces., Comment: 23 pages

In this paper, we study optimal quadrature errors, approximation numbers, and sampling numbers in $L_2(\Bbb S^d)$ for Sobolev spaces ${\rm H}^{\alpha,\beta}(\Bbb S^d)$ with logarithmic perturbation on the unit sphere $\Bbb S^d$ in $\Bbb R^{d+1}$. First we obtain strong equivalences of the approximation numbers for ${\rm H}^{\alpha,\beta}(\Bbb S^d)$ with $\alpha>0$, which gives a clue to Open problem 3 as posed by Krieg and Vyb\'iral in \cite{KV}. Second, for the optimal quadrature errors for ${\rm H}^{\alpha,\beta}(\Bbb S^d)$, we use the "fooling" function technique to get lower bounds in the case $\alpha>d/2$, and apply Hilbert space structure and Vyb\'iral's theorem about Schur product theory to obtain lower bounds in the case $\alpha=d/2,\,\beta>1/2$ of small smoothness, which confirms the conjecture as posed by Grabner and Stepanyukin in \cite{GS} and solves Open problem 2 in \cite{KV}. Finally, we employ the weighted least squares operators and the least squares quadrature rules to obtain approximation theorems and quadrature errors for ${\rm H}^{\alpha,\beta}(\Bbb S^d)$ with $\alpha>d/2$ or $\alpha=d/2,\,\beta>1/2$, which are order optimal., Comment: 24 pages

Using effective Lagrangians constrained by the heavy quark spin symmetry and chiral symmetry, for the light quarks, we analyze the $D^0 D^0\pi^+$, $\bar{D}^0D^0\pi^0$ and $D^0\bar{D}^{*0}$ invariant mass spectra. Performing a simultaneous analysis of the doubly charmed and charm-anti-charm states gives further insights into the nature of the $T^+_{cc}$ and $\chi^0_{c1}(3872)$, exotic hadrons. We find that both states lie below the respective $DD^*$/$D\bar{D}^*$ thresholds. Also, the contributions of the triangle and box diagrams are negligible., Comment: 5 pages, 5 figures

In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^{3}\times\mathbb{R}^{3}$, where the initial fluid density is allowed to vanish. We establish the uniform bound of the macroscopic density associated with the distribution function and prove the global existence and uniqueness of strong solutions to the Cauchy problem with vacuum for either small initial energy or large viscosity coefficient. The uniform boundedness and the presence of vacuum enable us to show that as the time evolves, the fluid velocity decays, while the distribution function concentrates towards a Dirac measure in velocity centred at $0$, with an exponential rate. In order to overcome the degeneracy in the momentum equations, we develop an energy argument based on higher order functional inequalities designed for fluid-particle coupled structures.

We investigate the diffusive relaxation limit and the time-asymptotic stability of the Jin-Xin model toward viscous conservation laws in $\mathbb{R}^d$ with $d\geq1$. First, we establish uniform regularity estimates with respect to both the time and the relaxation parameter $\varepsilon>0$, for initial data in hybrid Besov spaces based on general $L^{p}$-norms. This uniformity enables us to derive $\mathcal{O}(\varepsilon)$ bounds on the difference between solutions of the viscous conservation law and its associated Jin-Xin approximation, thus justifying the strong convergence of the Jin-Xin hyperbolic relaxation. Furthermore, under an additional condition on the initial data, for instance, that the low frequencies belong to $L^{p/2}(\mathbb{R}^{d})$, we show that the $L^{p}(\mathbb{R}^d)$-norm of the solution to the Jin-Xin model decays at the optimal rate $(1+t)^{-d/{2p}}$ while the $L^{p}(\mathbb{R}^d)$-norm of its difference with the solution of the associated viscous conservation law decays at the enhanced rate $\varepsilon(1+t)^{-d/{2p}-1/2}$., Comment: 39 pages

A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for low ones. This allows to derive a sharp description of the space-time decay of solutions for large time. However, such analysis relies heavily on the use of the Fourier transform that we avoid here, developing the "physical space version" of the hyperbolic hypocoercivity approach introduced by Beauchard and Zuazua, to prove new asymptotic results in the linear and nonlinear settings. The new physical space version of the hyperbolic hypocoercivity approach allows to recover the natural heat-like time-decay of solutions under sharp rank conditions, without employing Fourier analysis or $L^1$ assumptions on the initial data. Taking advantage of this Fourier-free framework, we establish new enhanced time-decay estimates for initial data belonging to weighted Sobolev spaces. These results are then applied to the nonlinear compressible Euler equations with linear damping. We also prove the logarithmic stability of the nonlinearly damped $p$-system.