The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all $n$-vertex $k$-uniform hypertrees, we determine the $k$-uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all $n$-vertex $k$-uniform unicyclic hypergraphs, we obtain the $k$-uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the $k$-uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.

We compute the mean value of derivatives of $L$-functions for cyclotomic characters in function fields. We also show the non-vanishing property of derivatives of $L$-functions for cyclotomic characters in function fields.

Let $S$ be a Burniat surface with $K_S^2 = 6$ and $\varphi$ be the bicanonical map of $S$. In this paper we show optimal lower bounds of log canonical thresholds of members of pluricanonical sublinear systems of $S$ via Klein group $G$ induced by $\varphi$. Indeed, for a positive even integer $m$, the log canonical threshold of members of an invariant (resp. anti-invariant) part of $|mK_S|$ is greater than or equal to $1/(2m)$ (resp. $1/(2m-2)$). For a positive odd integer $m$, the log canonical threshold of members of an invariant (resp. anti-invariant) part of $|mK_S|$ is greater than or equal to $1/(2m-5)$ (resp. $1/(2m)$). The inequalities are all optimal.

In this paper, we introduce pseudo-Carleson measure, a generalization of Carleson measure, for Fock spaces, and give sufficient and necessary conditions for a complex Borel measure to be pseudo-Carleson. We then give integral representations of functions in a Fock space, and use the measures to characterize boundedness and compactness of small Hankel operators on Fock spaces.

The existence of singular limit solutions is established for a nonlinear elliptic Kuramoto–Sivashinsky system with exponential nonlinearity and Navier boundary conditions, by means of the nonlinear domain decomposition method.

Inspired by Alves and Souto [2], we investigate the existence of nontrivial solutions to a class of fractional Schrödinger equations with potentials well. Taking the superlinear nonlinearities into consideration, we obtain the existence of nontrivial solutions by loosing monotonicity. Furthermore, a ground state solution is established.

In this article, by using Moser's twist theorem, we prove that all solutions of the equation $x'' + ax^{+} - bx^{-} + \varphi(x) = p(t)$ are bounded in the critical situation, where $p$ is a smooth periodic function, and $\varphi$ is bounded one.

In this paper, we consider the $p$-Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, infinite time blow up and asymptotic behavior of solutions in two cases $E(0) \lt d$ and $E(0) = d$. Furthermore, the infinite time blow up of solutions for the problem with $E(0) \gt 0$ ($\omega = 0$) is studied.

In this article, our efforts focus on finding the conditions for the existence of solutions of Mixed Stampacchia Variational Inequality Interval-valued Problem on Hadamard manifolds with monotonicity assumption by using KKM mappings. Conditions that allow us to prove the existence of equilibrium points in a market of perfect competition. We will identify solutions of Stampacchia variational problem and optimization problem with the interval-valued convex objective function, improving on previous results in the literature. We will illustrate the main results obtained with some examples and numerical results.

In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets of a vector space are cancellative elements. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the order cancellation law where the canceled set is weakly narrow. Also, we prove the order cancellation law for closed convex subsets of topological vector space where the canceled set has bounded Hausdorff-like distance from its recession cone. We topologically embed the semigroup of closed convex sets sharing a recession cone having bounded Hausdorff-like distance from it into a topological vector space. This result extends Bielawski and Tabor's generalization of Rådström theorem.