For general first-order quasilinear hyperbolic systems, based on the analysis of simple wave solutions along characteristic trajectories, the global two-sided exact boundary controllability is achieved in a relatively short controlling time.

In this paper, new proofs of two functional relations for the alternating analogues of Tornheim’s double zeta function are given. Using the functional relations, the author gives new proofs of some evaluation formulas found by Tsumura for these alternating series.

The authors investigate locally primitive bipartite regular connected graphs of order 18p. It is shown that such a graph is either arc-transitive or isomorphic to one of the Gray graph and the Tutte 12-cage.

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable over W ₂(k), if X and all prime divisors on X can be lifted simultaneously over W ₂(k). In this paper, the author gives a criterion for those cyclic covers over strongly liftable schemes that are still strongly liftable. As a corollary, cyclic covers over projective spaces of dimension at least three are strongly liftable over W ₂(k).

The authors establish a Serrin’s regularity criterion for the β-generalized dissipative surface quasi-geostrophic equation. More precisely, it is shown that if the smooth solution θ satisfies ∇θ ∈ L ^q(0, T;L ^q(R²)) with $\frac{\alpha }{q} + \frac{2}{p} \leqslant \alpha + \beta - 1$, then the solution θ can be smoothly extended after time T. In particular, when α + β ≥ 2, it is shown that if ∂yθ ∈ L ^q(0, T;L ^q(R²)) with $\frac{\alpha }{q} + \frac{2}{p} \leqslant \alpha + \beta - 1$, then the solution θ can also be smoothly extended after time T. This result extends the regularity result of Yamazaki in 2012.

In this paper, the Chow-type maximal inequality for conditional demimartingales is established. By using the Chow-type maximal inequality, the authors provide the maximal inequality for conditional demimartingales based on concave Young functions. At last, the moment inequalities for conditional demimartingales are established.

This paper deals with the conditional quantile estimation based on left-truncated and right-censored data. Assuming that the observations with multivariate covariates form a stationary α-mixing sequence, the authors derive the strong convergence with rate, strong representation as well as asymptotic normality of the conditional quantile estimator. Also, a Berry-Esseen-type bound for the estimator is established. In addition, the finite sample behavior of the estimator is investigated via simulations.

Let eλ(x) be a Neumann eigenfunction with respect to the positive Laplacian Δ on a compact Riemannian manifold M with boundary such that Δe _λ = λ² e _λ in the interior of M and the normal derivative of e _λ vanishes on the boundary of M. Let χλ be the unit band spectral projection operator associated with the Neumann Laplacian and f be a square integrable function on M. The authors show the following gradient estimate for χλ f as $\lambda \geqslant 1:{\left\| {\nabla {\chi _\lambda }{\kern 1pt} \left. f \right\|} \right._\infty } \leqslant C\left( {\lambda \left\| {{\chi _\lambda }{{\left. f \right\|}_\infty } + \left. {{\lambda ^{ - 1}}} \right\|} \right.\Delta {\chi _\lambda }{{\left. f \right\|}_\infty }} \right)$, where C is a positive constant depending only on M. As a corollary, the authors obtain the gradient estimate of eλ: For every λ ≥ 1, it holds that $\left\| {\nabla {{\left. {{e_\lambda }} \right\|}_\infty } \leqslant C\left. \lambda \right\|} \right.{\left. {{e_\lambda }} \right\|_\infty }$.

In this paper, it is proved that all the alternating groups A _p+5 are OD-characterizable and the symmetric groups S _p+5 are 3-fold OD-characterizable, where p+4 is a composite number and p + 6 is a prime and 5 ≠ p ∈ π(1000!).

This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation: ${u_t} = \Delta u + \nabla \phi \cdot \nabla u + a\left( x \right)u\ln u + b\left( x \right)u$ on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by −K (K ≥ 0), where φ is a C ² function, a(x) and b(x) are C ¹ functions with certain conditions.

In this paper, the authors define a harmonic Orlicz combination and a dual Orlicz mixed volume of star bodies, and then establish the dual Orlicz-Minkowski mixedvolume inequality and the dual Orlicz-Brunn-Minkowksi inequality.

The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.

This paper is concerned with the zeroMach number limit of the three-dimensional compressible viscous magnetohydrodynamic equations. More precisely, based on the local existence of the three-dimensional compressible viscous magnetohydrodynamic equations, first the convergence-stability principle is established. Then it is shown that, when the Mach number is sufficiently small, the periodic initial value problems of the equations have a unique smooth solution in the time interval, where the incompressible viscous magnetohydrodynamic equations have a smooth solution. When the latter has a global smooth solution, the maximal existence time for the former tends to infinity as the Mach number goes to zero. Moreover, the authors prove the convergence of smooth solutions of the equations towards those of the incompressible viscous magnetohydrodynamic equations with a sharp convergence rate.