We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of Matsumoto zeta-functions $\varphi_h(s)$ and a collection of periodic Hurwitz zeta-functions $\zeta(s,\alpha;\mathfrak{B})$ under the condition that the common difference of arithmetical progression $h \gt 0$ is such that $\exp \big\{ \frac{2\pi}{h} \big\}$ is a rational number and parameter $\alpha$ is a transcendental number.

We study independence of symplectic embeddings of the theory of Ekedahl–Oort stratifications on Shimura varieties of Hodge type, by comparing two different embeddings with a third one. The main results are as follows.

1. The Ekedahl–Oort stratification is independent of the choices of symplectic embeddings.

2. Under certain reasonable assumptions, there is certain functoriality for Ekedahl–Oort stratifications with respect to morphisms of Shimura varieties.

We investigate int-amplified endomorphisms on normal projective surfaces. We prove that the output of the equivariant MMP is either a Q-abelian surface, a (equivariant) quasi-étale quotient of a smooth projective surface, a Mori dream space, or a projective cone of an elliptic curve.

It was shown by Beauville that if the canonical map $\varphi_{|K_M|}$ of a complex smooth projective surface $M$ is generically finite, then $\operatorname{deg}(\varphi_{|K_M|}) \leq 36$. The first example of a surface with canonical degree $36$ was found by the second author. In this article, we show that for any surface which is a degree four Galois étale cover of a fake projective plane $X$ with the largest possible automorphism group $\operatorname{Aut}(X) = C_7:C_3$ (the unique non-abelian group of order $21$), the base locus of the canonical map is finite, and we verify that $35$ of these surfaces have maximal canonical degree $36$. We also classify all smooth degree four Galois étale covers of fake projective planes, which give possible candidates for surfaces of canonical degree $36$. Finally, we also confirm in this paper the optimal upper bound of the canonical degree of smooth threefolds of general type with sufficiently large geometric genus, related to earlier work of Hacon and Cai.

In this paper, we consider the condition number theory for a linear function of the solution to the constrained and weighted least squares problem. We first present two explicit expressions without Kronecker product of normwise condition number using the classical method for condition numbers. Then, we derive the explicit expression of mixed and componentwise condition numbers by the dual techniques. To estimate these condition numbers with high reliability, we choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method and devise three algorithms. Numerical experiments are provided to illustrate the obtained results.

We prove that for each nonseparable and reflexive Banach space $(X,\|\cdot\|_X)$ with the nonstrict Opial and Kadec–Klee properties, there exists an equivalent norm $\|\cdot\|_0$ such that the Banach space $(X,\|\cdot\|_0)$ is LUR and contains a diametrically complete set with empty interior.

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and an analytic function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued analytic function $f$, where $X$ is a Banach space. Some estimates for the norm of the operator $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtained. In particular, it is shown that the Volterra operator $J_b \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ is bounded if and only if $J_b \colon A^2_{\alpha} \to A^2_{\alpha}$ is in the Schatten class $S_p(A^2_{\alpha})$ for $2 \leq p \lt \infty$ and $\alpha \gt -1$. Some corresponding results are established for $X$-valued Hardy spaces and $X$-valued Fock spaces.

In this paper, we study the existence of semiclassical solutions of the fractional Schrödinger–Poisson system with critical exponent in $\mathbb{R}^{3}$. Under suitable assumptions, we show that the problem has at least one nontrivial solution provided that $\epsilon \leq \varepsilon_{\delta}$ where $\varepsilon_{\delta}$ is sufficiently small positive number.

In this paper, we construct a simple chemostat-based variable yield model of competition between two bacterial strains, one of which is capable of wall growth [14]. In this model we prove the boundedness of solutions, analyze the local stability of equilibria and establish the global stability for the locally stable extinction equilibrium. Furthermore, when the extinction equilibrium becomes unstable, we prove the existence and uniqueness of the positive equilibrium and the uniform persistence of the system.

In the present paper, we deal with the global regularity estimates for the $p$-Laplace equations with data in divergence form \[ \operatorname{div}(|\nabla u|^{p-2} \nabla u) = \operatorname{div}(|F|^{p-2} F) \quad \textrm{in $\Omega$}, \] in Morrey spaces with natural data $F \in L^p(\Omega;\mathbb{R}^n)$ and nonhomogeneous boundary data belongs to $W^{1,p}(\Omega)$. Motivated by the work of [M.-P. Tran, T.-N. Nguyen, New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data, J. Differential Equations 268 (2020), no. 4, 1427–1462], this paper extends that of global Lorentz–Morrey gradient estimates in which the `good-$\lambda$' technique was undertaken for a class of more general equations, and further, global regularity of weak solutions will be given in terms of fractional maximal operators.

This paper is concerned with traveling wave solutions in a discrete diffusion epidemic model with delayed transmission. Employing the way of contradictory discussions and the bilateral Laplace transform, we obtain the nonexistence of nontrivial positive bounded traveling wave solutions. Utilizing the super-/sub-solutions method and the fixed point theory, we derive the existence of nontrivial positive traveling wave solutions with both super-critical and critical speeds. Our results indicate that the critical speed is the minimal speed.